System and method for estimating tissue heating of a target ablation zone for electrical-energy based therapies

ABSTRACT

Systems and methods are provided for modeling and for providing a graphical representation of tissue heating and electric field distributions for medical treatment devices that apply electrical treatment energy through one or a plurality of electrodes. In embodiments, methods comprise: providing one or more parameters of a treatment protocol for delivering one or more electrical pulses to tissue through a plurality of electrodes; modeling electric and heat distribution in the tissue based on the parameters; and displaying a graphical representation of the modeled electric and heat distribution. In another embodiment, a treatment planning module is adapted to generate an estimated target ablation zone based on a combination of one or more parameters for an irreversible electroporation protocol and one or more tissue-specific conductivity parameters.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is a Continuation-in-Part (CIP) of U.S. patentapplication Ser. No. 14/012,832, filed on Aug. 28, 2013, which publishedas U.S. Pat. No. 9,283,051832, which CIP relies on and claims thebenefit of the filing date of U.S. Provisional Application No.61/694,144, filed on Aug. 28, 2012. Application Ser. No. 14/012,832 is aCIP of U.S. application Ser. No. 12/491,151, filed on Jun. 24, 2009,which published as U.S. Pat. No. 8,992,517, which relies on and claimsthe benefit of the filing dates of U.S. Provisional Patent ApplicationNos. 61/171,564, filed on Apr. 22, 2009, 61/167,997, filed on Apr. 9,2009, and 61/075,216, filed on Jun. 24, 2008. Application Ser. No.12/491,151 is also a CIP of U.S. patent application Ser. No. 12/432,295,filed on Apr. 29, 2009, now U.S. Pat. No. 9,598,691, which relies on andclaims the benefit of the filing date of U.S. Provisional PatentApplication No. 61/125,840, filed on Apr. 29, 2008. The presentapplication also relies on and claims priority to and the benefit of thefiling date of U.S. Provisional Application No. 61/910,655, filed Dec.2, 2013. The disclosures of these patent applications are herebyincorporated by reference herein in their entireties.

FIELD OF THE INVENTION

The present invention is related to medical therapies involving theadministering of electrical treatment energy. More particularly,embodiments of the present invention provide systems and methods formodeling and providing a graphical representation of tissue heating andelectric field for a medical treatment device that applies electricaltreatment energy through a plurality of electrodes defining a targettreatment area. Embodiments of the present invention also providesystems and methods providing a graphical representation of a targetablation zone based on one or more electrical conductivity parametersthat are specific for the tissue to be treated.

DESCRIPTION OF RELATED ART

Electroporation-based therapies (EBTs) are clinical procedures thatutilize pulsed electric fields to induce nanoscale defects in cellmembranes. Typically, pulses are applied through minimally invasiveneedle electrodes inserted directly into the target tissue, and thepulse parameters are tuned to create either reversible or irreversibledefects. Reversible electroporation facilitates the transport ofmolecules into cells without directly compromising cell viability. Thishas shown great promise for treating cancer when used in combinationwith chemotherapeutic agents or plasmid DNA (M. Marty et al.,“Electrochemotherapy—An easy, highly effective and safe treatment ofcutaneous and subcutaneous metastases: Results of ESOPE (EuropeanStandard Operating Procedures of Electrochemotherapy) study,” EuropeanJournal of Cancer Supplements, 4, 3-13, 2006; A. I. Daud et al., “PhaseI Trial of Interleukin-12 Plasmid Electroporation in Patients WithMetastatic Melanoma,” Journal of Clinical Oncology, 26, 5896-5903, Dec.20, 2008). Alternatively, irreversible electroporation (IRE) has beenrecognized as a non-thermal tissue ablation modality that produces atissue lesion, which is visible in real-time on multiple imagingplatforms (R. V. Davalos, L. M. Mir, and B. Rubinsky, “Tissue ablationwith irreversible electroporation,” Ann Biomed Eng, 33, 223-31, February2005; R. V. Davalos, D. M. Otten, L. M. Mir, and B. Rubinsky,“Electrical impedance tomography for imaging tissue electroporation,”IEEE Transactions on Biomedical Engineering, 51, 761-767, 2004; L.Appelbaum, E. Ben-David, J. Sosna, Y. Nissenbaum, and S. N. Goldberg,“US Findings after Irreversible Electroporation Ablation:Radiologic-Pathologic Correlation,” Radiology, 262, 117-125, Jan. 1,2012). Because the mechanism of cell death does not rely on thermalprocesses, IRE spares major nerve and blood vessel architecture and isnot subject to local heat sink effects when using a specific protocolthat does not exceed the thermal damage threshold. (B. Al-Sakere, F.Andre, C. Bernat, E. Connault, P. Opolon, R. V. Davalos, B. Rubinsky,and L. M. Mir, “Tumor ablation with irreversible electroporation,” PLoSONE, 2, e1135, 2007). These unique benefits have translated to thesuccessful treatment of several surgically “inoperable” tumors (K. R.Thomson et al., “Investigation of the safety of irreversibleelectroporation in humans,” J Vasc Intery Radiol, 22, 611-21, May 2011;R. E. Neal II et al., “A Case Report on the Successful Treatment of aLarge Soft-Tissue Sarcoma with Irreversible Electroporation,” Journal ofClinical Oncology, 29, 1-6, 2011; P. A. Garcia et al., “Non-thermalirreversible electroporation (N-TIRE) and adjuvant fractionatedradiotherapeutic multimodal therapy for intracranial malignant glioma ina canine patient,” Technol Cancer Res Treat, 10, 73-83, 2011).

In EBTs, the electric field distribution is the primary factor fordictating defect formation and the resulting volume of treated tissue(J. F. Edd and R. V. Davalos, “Mathematical modeling of irreversibleelectroporation for treatment planning,” Technology in Cancer Researchand Treatment, 6, 275-286, 2007 (“Edd and Davalos, 2007”); D. Miklavcic,D. Semrov, H. Mekid, and L. M. Mir, “A validated model of in vivoelectric field distribution in tissues for electrochemotherapy and forDNA electrotransfer for gene therapy,” Biochimica et Biophysica Acta,1523, 73-83, 2000). The electric field is influenced by both thegeometry and positioning of the electrodes as well as the dielectrictissue properties. Because the pulse duration is typically much longerthan the pulse rise/fall time, static solutions of the Laplace'sequation incorporating only electric conductivity are sufficient forpredicting the electric field distribution. In tissues with uniformconductivity, solutions can be obtained analytically for various needleelectrode configurations if the exposure length is much larger than theseparation distance (S. Corovic, M. Pavlin, and D. Miklavcic,“Analytical and numerical quantification and comparison of the localelectric field in the tissue for different electrode configurations,”Biomed Eng Online, 6, 2007; R. Neal II et al., “ExperimentalCharacterization and Numerical Modeling of Tissue ElectricalConductivity during Pulsed Electric Fields for IrreversibleElectroporation Treatment Planning,” Biomedical Engineering, IEEETransactions on, PP, 1-1, 2012 (“Neal et al., 2012”)). This is not oftenthe case in clinical applications where aberrant masses with a diameteron the order of 1 cm are treated with an electrode exposure length ofsimilar dimensions. Additionally, altered membrane permeability due toelectroporation influences the tissue conductivity in a non-linearmanner. Therefore numerical techniques may be used to account for anyelectrode configuration and incorporate a tissue-specific functionrelating the electrical conductivity to the electric field distribution(i.e. extent of electroporation).

Conventional devices for delivering therapeutic energy such aselectrical pulses to tissue include a handle and one or more electrodescoupled to the handle. Each electrode is connected to an electricalpower source. The power source allows the electrodes to deliver thetherapeutic energy to a targeted tissue, thereby causing ablation of thetissue.

Once a target treatment area is located within a patient, the electrodesof the device are placed in such a way as to create a treatment zonethat surrounds the treatment target area. In some cases, each electrodeis placed by hand into a patient to create a treatment zone thatsurrounds a lesion. The medical professional who is placing theelectrodes typically watches an imaging monitor while placing theelectrodes to approximate the most efficient and accurate placement.

However, if the electrodes are placed by hand in this fashion, it isvery difficult to predict whether the locations selected will ablate theentire treatment target area because the treatment region defined by theelectrodes vary greatly depending on such parameters as the electricfield density, the voltage level of the pulses being applied, size ofthe electrode and the type of tissue being treated. Further, it is oftendifficult or sometimes not possible to place the electrodes in thecorrect location of the tissue to be ablated because the placementinvolves human error and avoidance of obstructions such as nerves, bloodvessels and the like.

Conventionally, to assist the medical professional in visualizing atreatment region defined by the electrodes, an estimated treatmentregion is generated using a numerical model analysis such as complexfinite element analysis. One problem with such a method is that even amodest two dimensional treatment region may take at least 30 minutes toseveral hours to complete even in a relatively fast personal computer.This means that it would be virtually impossible to try to obtain on areal time basis different treatment regions based on different electrodepositions.

In IRE treatments, the electric field distribution is the primary factorfor dictating defect formation and the resulting volume of treatedtissue (See J. F. Edd and R. V. Davalos, “Mathematical modeling ofirreversible electroporation for treatment planning,” Technol Cancer ResTreat, vol. 6, pp. 275-286, 2007; D. Sel, et al., “Sequential finiteelement model of tissue electropermeabilization,” IEEE Trans Biomed Eng,vol. 52, pp. 816-27, May 2005). The electric field is influenced by boththe geometry and positioning of the electrodes as well as the dielectrictissue properties. The application of an electric field across anyconductive media will result in some degree of resistive losses in whichenergy is dissipated as heat. Though cell death in IRE is attributed tonon-thermal mechanisms, it is possible to inadvertently elevate tissuetemperatures above thermal damage thresholds if parameters are notchosen carefully. Since a major advantage of IRE is the ablation oftissue without deleterious thermal effects and the therapy is oftenapplied in regions which cannot clinically sustain thermal injury, it isimportant to identify safe operating parameters. Transient heating oftissue in proximity to the electrode can result in the denaturing of theextracellular matrix, scar formation, or damage to local blood vesselsand nerves. To avoid these effects, it is important to understand theextent and geometry of tissue heating.

Therefore, it would be desirable to provide an improved system andmethod to predict a treatment region that avoids electrical and thermaloverexposure and damage in order to determine safe and effective pulseprotocols for administering electrical energy based therapies, such IRE.

SUMMARY OF THE INVENTION

In one embodiment, the invention provides a system for treating atissue, which system applies electrical treatment energy through one ormore electrodes, such as a plurality of electrodes, defining a targettreatment area of the tissue. The system comprises a memory, a displaydevice, a processor coupled to the memory and the display device, and atreatment planning module stored in the memory and executable by theprocessor. In one embodiment, the treatment planning module is adaptedto generate an estimated heat distribution and/or electrical fielddistribution in the display device based on one or more parameters foran electrical energy based protocol, such as an irreversibleelectroporation (IRE) protocol. In another embodiment, the treatmentplanning module is adapted to generate an estimated target ablation zonebased on a combination of one or more parameters for an electricalenergy based protocol, such as an IRE-based protocol, and one or moretissue-specific conductivity parameters.

In another embodiment, the invention provides a method of treating atissue with a medical treatment device that applies electrical treatmentenergy through a one or more or a plurality of electrodes defining atarget treatment area of the tissue and comprises a display device. Themethod may be executed partially or completely using the system of theinvention. In a specific embodiment, one or more steps are executedthrough the treatment planning module.

In embodiments, the treatment planning module can be used to determine atemperature distribution to determine tissue heating at or around atarget ablation zone prior to or during treatment. The treatmentplanning module can be used to graphically display contour lines whichrepresent a specific temperature of tissue heating. In one embodiment,the treatment planning module estimates the temperature rise withintissue due to Joule heating effects, and plots a contour line accordingto a temperature specified by a user. Further, the treatment planningmodule may further plot a contour line representing an electric fieldintensity such that temperature and electric field intensity can becorrelated. The treatment planning module may plot the temperaturedistribution and electric field distribution for a bipolar and singleneedle electrodes. This capability may allow a user (e.g. treatingphysician) to determine heating to surrounding tissues during treatmentplanning and adjust parameters to prevent thermal damage to criticalsurrounding structures such as nerves and blood vessels. In oneembodiment, the contour lines are Cassini oval approximations performedaccording to the equations and procedure in Example 7.

In embodiments, the treatment planning module can be used to provide theelectric field distributions using different configurations of bipolarprobes and include the dynamic change in electrical conductivity fromthe non-electroporated baseline tissue electrical conductivity. Thetreatment planning module may plot contour lines representing electricfield distributions based on a specific combination of electrode length,separation distance, and applied voltage. The treatment planning modulemay incorporate the dynamic change in electrical conductivity from thebaseline during treatment to account for treatment-related changes inconductivity for particular tissues such as liver, kidney, brain, etc.This capability may allow the treating physician to determine electricfield distributions and zones of ablation based on the capacity for aspecific target tissue to change in conductivity during treatment. Inone embodiment, the contour lines are Cassini oval approximationsperformed according to the equations and procedure in Example 7.

In embodiments, the treatment planning module can be based on aparametric study of the dynamic conductivity curve so that variablesrelated to the dynamic conductivity could be used to fit tissue specificbehavior. In embodiments, the treatment planning module may provideinput for one or more electrical conductivity parameters such as thebaseline (e.g., non-electroporated) conductivity, change inconductivity, the transition zone (how rapidly the conductivityincreases), the electric field at which the change in conductivityoccurs, and the electric field at which irreversible electroporationoccurs. These parameters may be experimentally derived for differenttissues and stored in a database. This capability may allow the treatingphysician to account for different conductivity parameters as they applyto different target tissues when designing a treatment protocol. Thus,when considering a specific tissue, the treating physician may optimizethe calculation of an ablation zone for that tissue by inputting one ormore of the tissue-specific conductivity parameters for the tissue ofinterest.

BRIEF DESCRIPTION OF THE DRAWINGS The accompanying drawings illustratecertain aspects of embodiments of the present invention, and should notbe used to limit or define the invention. Together with the writtendescription the drawings serve to explain certain principles of theinvention.

FIG. 1 is a schematic diagram of a representative system of theinvention.

FIG. 2 is a schematic diagram of a representative treatment controlcomputer of the invention.

FIG. 3 is schematic diagram illustrating details of the generator shownin the system of FIG. 1, including elements for detecting anover-current condition.

FIG. 4 is a schematic diagram showing IRE zones of ablation nomenclature(see E. Ben-David, et al., “Characterization of IrreversibleElectroporation Ablation in In Vivo Porcine Liver,” Am J Roentgenol,vol. 198, pp. W62-W68, January 2012).

FIG. 5 is a graph of the asymmetrical Gompertz function showing tissueelectric conductivity as a function of electric field.

FIG. 6 is a graph showing a representative 3D plot of current [A] as afunction of Z (σ_(max)/σ₀) and voltage-to-distance ratio (W) for aseparation distance of 1.5 cm and an electrode exposure length of 2.0 cmas used by Ben-David et al.

FIGS. 7A and 7B are graphs showing representative contour plots ofcurrent [A] as a function of electrode exposure and separation distanceusing 1500 V/cm for Z=1 (FIG. 7A) and Z=4 (FIG. 7B).

FIGS. 8A and 8B are tables showing Whole Model Parameter Estimates andEffect Tests, respectively.

FIG. 8C is a graph showing a plot of Actual Current vs. PredictedCurrent.

FIGS. 9A-9E are graphs showing the representative (15 mm gap)correlation between current vs. exposure length and electrode radius formaximum electrical conductivities (1×-6×, respectively).

FIG. 10A is a table showing experimental validation of the code fordetermining the tissue/potato dynamic from in vitro measurements,referred to as potato experiment #1.

FIG. 10B is a table showing experimental validation of the code fordetermining the tissue/potato dynamic from in vitro measurements,referred to as potato experiment #2.

FIGS. 11A and 11B are graphs plotting residual current versus data pointfor analytical shape factor (FIG. 11A) and statistical (numerical)non-linear conductivity (FIG. 11B).

FIGS. 12A-12C are graphs showing representative contour plots of theelectric field strength at 1.0 cm from the origin using an edge-to-edgevoltage-to-distance ratio of 1500 V/cm assuming z=1, wherein FIG. 12A isa plot of the x-direction, FIG. 12B is a plot of the y-direction, andFIG. 12C is a plot of the z-direction.

FIGS. 13A-13C are 3D plots representing zones of ablation for a 1500V/cm ratio, electrode exposure of 2 cm, and electrode separation of 1.5cm, at respectively a 1000 V/cm IRE threshold (FIG. 13A), 750 V/cm IREthreshold (FIG. 13B), and 500 V/cm IRE threshold (FIG. 13C) using theequation for an ellipsoid.

FIG. 14A is a schematic diagram showing an experimental setup of anembodiment of the invention.

FIG. 14B is a schematic diagram showing dimension labeling conventions.

FIG. 14C is a waveform showing 50 V pre-pulse electrical current at 1 cmseparation, grid=0.25 A, where the lack of rise in intrapulseconductivity suggests no significant membrane electroporation duringpre-pulse delivery.

FIG. 14D is a waveform showing electrical current for pulses 40-50 of1750 V at 1 cm separation, grid=5 A, where progressive intrapulsecurrent rise suggests continued conductivity increase andelectroporation.

FIGS. 15A and 15B are electric field [V/cm] isocontours fornon-electroporated tissue (FIG. 15A) and electroporated tissue (FIG.15B) maps assuming a maximum conductivity to baseline conductivity ratioof 7.0×.

FIGS. 16A and 16B are representative Cassini Oval shapes when varyingthe ‘a=0.5 (red), 0.6 (orange), 0.7 (green), 0.8 (blue), 0.9 (purple),1.0 (black)’ or ‘b=1.0 (red), 1.05 (orange), 1.1 (green), 1.15 (blue),1.2 (purple), 1.25 (black)’ parameters individually. Note: If a>1.0 orb<1.0 the lemniscate of Bernoulli (the point where the two ellipsesfirst connect (a=b=1) forming “∞”) disconnects forming non-contiguousshapes.

FIG. 17 is a graph showing NonlinearModelFit results for the ‘a’ and ‘b’parameters used to generate the Cassini curves that represent theexperimental IRE zones of ablation in porcine liver.

FIG. 18 shows Cassini curves from a ninety 100-μs pulse IRE treatmentthat represent the average zone of ablation (blue dashed), +SD (redsolid), and −SD (black solid) according to a=0.821±0.062 andb=1.256±0.079 using two single needle electrodes.

FIG. 19 is a representation of the Finite Element Analysis (FEA) modelfor a 3D Electric Field [V/cm] Distribution in Non-Electroporated(Baseline) Tissue with 1.5-cm Single Needle Electrodes at a Separationof 2.0 cm and with 3000 V applied.

FIGS. 20A-D are representations of the Electric Field [V/cm]Distributions from the 3D Non-Electroporated (Baseline) Models of FIG.19, wherein FIG. 20A represents the x-y plane mid-electrode length, FIG.20B represents the x-z plane mid-electrode diameter, FIG. 20C representsthe y-z plane mid-electrode diameter, and FIG. 20D represents the y-zplane between electrodes.

FIG. 21 is a representation of the Finite Element Analysis (FEA) modelfor a 3D Electric Field [V/cm] Distribution in Electroporated Tissuewith 1.5-cm Single Needle Electrodes at a Separation of 2.0 cm and 3000V applied assuming σ_(max)/σ₀=3.6.

FIGS. 22A-22D are representations of the Electric Field [V/cm]Distributions from the 3D Electroporated Models with 1.5-cm Electrodesat a Separation of 2.0 cm and 3000 V (cross-sections) assumingσ_(max)/σ₀=3.6, wherein FIG. 22A represents the x-y plane mid-electrodelength, FIG. 22B represents the x-z plane mid-electrode diameter, FIG.22C represents the y-z plane mid-electrode diameter, and FIG. 22Drepresents the y-z plane between electrodes.

FIG. 23 is a representative Cassini curve showing zones of ablationderived using two single needle electrodes and the pre-pulse procedureto determine the ratio of maximum conductivity to baseline conductivity.For comparison purposes the baseline electric field isocontour is alsopresented in which no electroporation is taken into account.

FIGS. 24A-24D are representative surface plots showing finite elementtemperature calculations at different electrode spacings. The surfaceplots show temperature distributions at t=90 seconds (Ninety pulses of100 μs each) for 3000 V treatments with (A) 1.0 cm, (B) 1.5 cm, (C) 2.0cm, and (D) 2.5 cm electrode spacing. Contour lines show approximateelectric field correlating to T=45° C. (A) 900 V/cm, (B) 1075 V/cm, (C)1100 V/cm, and (D) 1080 V/cm.

FIGS. 25A-25D are representative surface plots showing Cassini OvalApproximations at different electrode spacings. The surface plots showthe temperature distribution at t=90 seconds (Ninety pulses of 100 μseach) for 3000 V treatments with (A) 1.0 cm, (B) 1.5 cm, (C) 2.0 cm, and(D) 2.5 cm electrode spacing. Red dashed lines show the Cassini ovalcorrelating to T=45° C. and the black dotted lines show the Cassini ovalcorrelating to 500 V/cm.

FIGS. 26A-26D are representative surface plots showing Cassini OvalApproximations at different times. The surface plots show thetemperature distribution at (A) t=10 seconds, (B) t=40 seconds, (C) t=90seconds, and (D) t=200 seconds. Treatment parameters were held constantat 3000 V, 1.5 cm exposure, and 2.5 cm electrode spacing. Red dashedlines show the Cassini oval correlating to T=45° C. and the black dottedlines show the Cassini oval correlating to 500 V/cm. The pulses wereprogrammed with 100 μs duration.

FIGS. 27A-27D are representative surface plots showing Cassini OvalApproximations at different temperatures. The surface plots show thetemperature distribution at A) T=37.2° C., B) T=40° C., C) T=45° C., andD) T=50° C. Treatment parameters were held constant at 3000V, 1.5 cmexposure, and 2.5 cm electrode spacing at a time=90 seconds (Ninetypulses of 100 μs each). Red dashed lines show the Cassini ovalcorrelating to the specified temperatures and the black dotted linesshow the Cassini oval correlating to 500 V/cm.

FIG. 28 is a screenshot of the Cassini Oval Approximation Tool using thefollowing parameters: Voltage=3000 V, Gap=10 mm, Time=90 seconds (Ninetypulses of 100 μs each), Temperature=50° C., and Electric Field=500 V/cm.The red dashed line shows the Cassini oval correlating to 50° C. and theblack dotted lines show the Cassini oval correlating to 500 V/cm.

FIG. 29 is a screenshot of the Cassini Oval Approximation Tool using thefollowing parameters: Voltage=3000 V, Gap=10 mm, Time=90 seconds (Ninetypulses of 100 μs each), Temperature=40° C., and Electric Field=500 V/cm.The red dashed lines show the Cassini oval correlating to 40° C. and theblack dotted line show the Cassini oval correlating to 500 V/cm.

FIGS. 30A-30D are representative surface plots showing Cassini OvalApproximations at different temperature thresholds. The surface plotsshow the temperature and electric field distribution at A) T=40° C., B)T=45° C., C) T=50° C., and D) T=55° C. The other parameters are the sameas those for FIGS. 28 and 29. The red dashed lines show the Cassini ovalcorrelating to the specified temperatures and the black dotted linesshow the Cassini oval correlating to 500 V/cm.

FIGS. 31A-31D are representative surface plots showing Cassini OvalApproximations at different voltages. The surface plots show thetemperature and electric field distribution at A) 3000 V, B) 2000 V C)1500 V and D) 1000 V. Other parameters were Gap=10 mm, Time=90 seconds(Ninety pulses of 100 μs each), Temperature=40° C., and ElectricField=500 V/cm. The red dashed lines show the Cassini oval correlatingto 40° C. and the black dotted lines show the Cassini oval correlatingto 500 V/cm.

FIGS. 32A-32D are representative surface plots showing Cassini OvalApproximations at different electric field thresholds. The surface plotsshow the temperature and electric field distribution at A) 500 V/cm, B)1000 V/cm, C) 1500 V/cm, and D) 2000 V/cm. Other parameters wereVoltage=3000 V, Gap=10 mm, Time=90 seconds (Ninety pulses of 100 μseach), Temperature=40° C. The red dashed lines show the Cassini ovalcorrelating to 40° C. and the black dotted lines show the Cassini ovalcorrelating to the specified electric field thresholds.

FIGS. 33A-33D are representative surface plots showing Cassini OvalApproximations at different electrode spacings. The surface plots showthe temperature and electric field distribution at an electrode spacingof 5 mm, 10 mm, 15 mm, and 20 mm. Other parameters were Voltage=3000 V,Time=90 seconds (Ninety pulses of 100 μs each), Temperature=40° C., andElectric Field=500 V/cm. The red dashed lines show the Cassini ovalcorrelating to 40° C. and the black dotted lines show the Cassini ovalcorrelating to 500 V/cm.

FIGS. 34A-34D are representative surface plots showing Cassini OvalApproximations at different times. The surface plots show thetemperature and electric field distribution at A) 90 seconds (Ninetypulses of 100 μs each), B) 60 seconds (Sixty pulses of 100 μs each), C)30 seconds (Thirty pulses of 100 μs each), and D) 10 seconds (Ten pulsesof 100 μs each). Other parameters were Voltage=3000 V, Gap=10 mm,Temperature=40° C., and Electric Field=500 V/cm. The red dashed linesshow the Cassini oval correlating to 40° C. and the black dotted linesshow the Cassini oval correlating to 500 V/cm.

FIG. 35 is a representation of the COMSOL three-dimensional finiteelement domain and mesh used to calculate Cassini Oval values for theelectric and thermal curves.

FIGS. 36A-36C show a representation of a visualization tool providingthe 650 V/cm electric field distributions using different configurationsof bipolar probes and includes dynamic change (3.6×) in electricalconductivity from the non-electroporated baseline for runs 7, 8, and 9of the visualization.

FIG. 36D is a table showing parameters of runs 7, 8, and 9 includingelectrode length, separation distance (insulation), and applied voltage.

FIG. 36E is a table showing lesion dimensions for runs 7, 8, and 9. Theresults show that as the length of the bipolar electrode increases thesize of the zone of ablation increases.

FIG. 37 is a graph showing electrical conductivity (S/m, y-axis) plottedagainst electric field strength (V/cm, x-axis). FIG. 37 shows theconductivity changes from 0.1 to 0.35 at an electric field centered at500 V/cm.

FIG. 38A is a representative contour plot showing the “Goldberg” data(red dashed line) vs a calculated threshold (solid black line) based onthe parameters shown in FIG. 38C. The x and y axes represent distance[cm].

FIG. 38B is a representative contour plot showing the conductivity (bluedotted line) vs. a calculated threshold (solid black line) based on theparameters shown in FIG. 38C. The x and y axes represent distance [cm].

FIG. 38C is a table showing the parameters used to generate the contourplots of FIGS. 38A and 38B.

FIGS. 39A-39C are representative contour plots showing the “Goldberg”data (red dashed line) and calculated threshold (solid black line) andFIGS. 39D-39F are contour plots showing the conductivity (blue dottedline) and calculated threshold (solid black line) for conductivities of2, 3, and 4, respectively. The other parameters are the same as those inthe table of FIG. 38C. The x and y axes represent distance [cm].

FIGS. 40A-40C are representative contour plots showing the “Goldberg”data (red dashed line) and calculated threshold (solid black line) andFIGS. 40D-40F are contour plots showing the conductivity (blue dottedline) and calculated threshold (solid black line) for conductivitymultipliers of 2, 3, and 4, respectively. Other parameters used togenerate the plots of FIGS. 40A-40F include an IRE Threshold of 600V/cm, a transition zone of 0.4, a Voltage of 700 V, an E-Field of 700V/cm, and a Sigma (baseline electrical conductivity) of 0.20 S/m. The xand y axes represent distance [cm].

FIGS. 41A-41C are representative contour plots showing the “Goldberg”data (red dashed line) and calculated threshold (solid black line) andFIGS. 41D-41F are contour plots showing the conductivity (blue dottedline) and calculated threshold (solid black line) for conductivitymultipliers of 2, 3, and 4, respectively. Other parameters used togenerate the plots of FIGS. 41A-41F include an IRE Threshold of 1000V/cm, transition zone of 0.2, Voltage of 2700 V, E-Field of 700 V/cm,and Sigma (baseline electrical conductivity) of 0.20 S/m. The x and yaxes represent distance [cm].

FIG. 42 is a representative contour plot of the electric fielddistribution assuming a static electrical conductivity using a bipolarprobe. The model assumes an applied voltage of 2700 V with 7 mm longelectrodes separated by an 8 mm insulation shaft.

FIGS. 43A-43D are representative contour plots of post-IRE cellviability predictions with the colored curves illustrating differentcell viability levels. The model assumes using ninety 100-μs pulses at arate of one pulse per second with 2700 V, and a viability value of 0.1%(S=0.001) as the complete cell death due to IRE exposure.

FIG. 44 is a graph showing the dynamic electric conductivity function ofliver tissue undergoing electroporation. The sigmoid function includes abaseline of 0.067 S/m and maximum conductivity of 0.241 S/m.

FIG. 45 is a representative contour plot showing the electric fielddistribution assuming a dynamic electrical conductivity using thebipolar probe with 3000 V with 7 mm long electrodes separated by an 8 mminsulation shaft.

FIGS. 46A-D are representative contour plots showing post-IRE cellviability, wherein A) corresponds to 20 pulses at 2000 volts, B)corresponds to 20 pulses at 3000 volts, C) corresponds to 100 pulses at2000 volts, and D) corresponds to 100 pulses at 3000 volts.

FIGS. 47A and 47B are representative contour plots showing post-IRE cellviability after three hundred (FIG. 47A) and three hundred and sixty(FIG. 47B) 100-μs pulses at a rate of one pulse per second with anapplied voltage of 3000 V.

FIGS. 48A and 48B are a table showing the results of a parametric studyon bipolar electrode configuration as a function of electrode length,separation distance, and diameter in the resulting IRE area and volume.

FIG. 49 is a table showing the results of a parametric study on bipolarelectrode configuration as a function of applied voltage and pulsenumber in the resulting IRE area and volume with 7 mm long electrodesseparated by an 8 mm insulation shaft.

FIG. 50 is a table showing the results of a parametric study on bipolarelectrode configuration as a function of pulse number in the resultingIRE area and volume with an applied voltage of 3000 V with 7 mm longelectrodes separated by an 8 mm insulation shaft.

FIGS. 51A-C are schematics of representative electrode geometries.

FIGS. 51D-F are representative contour plots showing the resultingelectric field distribution corresponding to the electrode geometries ofFIGS. 51A-C.

DETAILED DESCRIPTION OF VARIOUS EMBODIMENTS OF THE INVENTION

Reference will now be made in detail to various exemplary embodiments ofthe invention. Embodiments described in the description and shown in thefigures are illustrative only and are not intended to limit the scope ofthe invention. Changes may be made in the specific embodiments describedin this specification and accompanying drawings that a person ofordinary skill in the art will recognize are within the scope and spiritof the invention.

Throughout the present teachings, any and all of the features and/orcomponents disclosed or suggested herein, explicitly or implicitly, maybe practiced and/or implemented in any combination, whenever andwherever appropriate as understood by one of ordinary skill in the art.The various features and/or components disclosed herein are allillustrative for the underlying concepts, and thus are non-limiting totheir actual descriptions. Any means for achieving substantially thesame functions are considered as foreseeable alternatives andequivalents, and are thus fully described in writing and fully enabled.The various examples, illustrations, and embodiments described hereinare by no means, in any degree or extent, limiting the broadest scopesof the claimed inventions presented herein or in any future applicationsclaiming priority to the instant application.

Embodiments of the invention include a method for visualization of heatand electric field distribution within a target treatment area, themethod comprising: selecting as inputs an applied voltage, electrodespacing, and treatment duration corresponding to a desired treatmentprotocol for a target treatment area; using the inputs in a Cassiniapproximation of data, wherein the data comprises measured voltage,electrode spacing, and time of actual treatment protocols, anddetermining an expected temperature distribution and expected electricfield distribution of the target treatment area; and displaying agraphical representation of a selected temperature and a selectedelectric field of the expected temperature and electric fielddistributions. Such methods can further comprise as inputs one or moreof a baseline conductivity for the target treatment area, a change inconductivity for the target treatment area, or a conductivity for aspecific tissue type.

Such methods can include a method of treatment planning for medicaltherapies involving administering electrical treatment energy, themethod comprising: providing one or more parameters of a treatmentprotocol for delivering one or more electrical pulses to tissue throughone or more or a plurality of electrodes; modeling heat distribution inthe tissue based on the parameters; and displaying a graphicalrepresentation of the modeled heat distribution.

One embodiment of the present invention is illustrated in FIGS. 1 and 2.Representative components that can be used with the present inventioncan include one or more of those that are illustrated in FIG. 1. Forexample, in embodiments, one or more probes 22 can be used to delivertherapeutic energy and are powered by a voltage pulse generator 10 thatgenerates high voltage pulses as therapeutic energy such as pulsescapable of irreversibly electroporating the tissue cells. In theembodiment shown, the voltage pulse generator 10 includes six separatereceptacles for receiving up to six individual probes 22 which areadapted to be plugged into the respective receptacle. The receptaclesare each labeled with a number in consecutive order. In otherembodiments, the voltage pulse generator can have any number ofreceptacles for receiving more or less than six probes.

For example, a treatment protocol according to the invention couldinclude a one or more or a plurality of electrodes. According to thedesired treatment pattern, the plurality of electrodes can be disposedin various positions relative to one another. In a particular example, aplurality of electrodes can be disposed in a relatively circular patternwith a single electrode disposed in the interior of the circle, such asat approximately the center. Any configuration of electrodes is possibleand the arrangement need not be circular but any shape periphery can beused depending on the area to be treated, including any regular orirregular polygon shape, including convex or concave polygon shapes. Thesingle centrally located electrode can be a ground electrode while theother electrodes in the plurality can be energized. Any number ofelectrodes can be in the plurality such as from about 1 to 20. Indeed,even 3 electrodes can form a plurality of electrodes where one groundelectrode is disposed between two electrodes capable of being energized,or 4 electrodes can be disposed in a manner to provide two electrodepairs (each pair comprising one ground and one electrode capable ofbeing energized). During treatment, methods of treating can involveenergizing the electrodes in any sequence, such as energizing one ormore electrode simultaneously, and/or energizing one or more electrodein a particular sequence, such as sequentially, in an alternatingpattern, in a skipping pattern, and/or energizing multiple electrodesbut less than all electrodes simultaneously, for example.

In the embodiment shown, each probe 22 includes either a monopolarelectrode or bipolar electrodes having two electrodes separated by aninsulating sleeve. In one embodiment, if the probe includes a monopolarelectrode, the amount of exposure of the active portion of the electrodecan be adjusted by retracting or advancing an insulating sleeve relativeto the electrode. See, for example, U.S. Pat. No. 7,344,533, which isincorporated by reference herein in its entirety. The pulse generator 10is connected to a treatment control computer 40 having input devicessuch as keyboard 12 and a pointing device 14, and an output device suchas a display device 11 for viewing an image of a target treatment areasuch as a lesion 300 surrounded by a safety margin 301. The therapeuticenergy delivery device 22 is used to treat a lesion 300 inside a patient15. An imaging device 30 includes a monitor 31 for viewing the lesion300 inside the patient 15 in real time. Examples of imaging devices 30include ultrasonic, CT, MRI and fluoroscopic devices as are known in theart.

The present invention includes computer software (treatment planningmodule 54) which assists a user to plan for, execute, and review theresults of a medical treatment procedure, as will be discussed in moredetail below. For example, the treatment planning module 54 assists auser to plan for a medical treatment procedure by enabling a user tomore accurately position each of the probes 22 of the therapeutic energydelivery device 20 in relation to the lesion 300 in a way that willgenerate the most effective treatment zone. The treatment planningmodule 54 can display the anticipated treatment zone based on theposition of the probes and the treatment parameters. The treatmentplanning module 54 may also display a zone of temperature heatingaccording to cutoff values inputted by the treating physician andcorrelate this with a value for the electric field distribution. Thetreatment planning module may also allow the treating physician todisplay the anticipated treatment zone, or target ablation zone,according to one or more tissue-specific conductivity parametersinputted by the treating physician. The conductivity parameters mayinclude the baseline conductivity of the tissue to be treated, the ratioof the baseline conductivity to the maximum conductivity of the tissuethat is reached during treatment, the rate at which the conductivityincreases from the baseline to the maximum conductivity, and/or theelectric field at which the conductivity changes during treatment.

The treatment planning module 54 can display the progress of thetreatment in real time and can display the results of the treatmentprocedure after it is completed. This information can be displayed in amanner such that it can be used for example by a treating physician todetermine whether the treatment was successful and/or whether it isnecessary or desirable to re-treat the patient.

For purposes of this application, the terms “code”, “software”,“program”, “application”, “software code”, “computer readable code”,“software module”, “module” and “software program” are usedinterchangeably to mean software instructions that are executable by aprocessor. The “user” can be a physician or other medical professional.The treatment planning module 54 executed by a processor outputs variousdata including text and graphical data to the monitor 11 associated withthe generator 10.

Referring now to FIG. 2, the treatment control computer 40 of thepresent invention manages planning of treatment for a patient. Thecomputer 40 is connected to the communication link 52 through an I/Ointerface 42 such as a USB (universal serial bus) interface, whichreceives information from and sends information over the communicationlink 52 to the voltage generator 10. The computer 40 includes memorystorage 44 such as RAM, processor (CPU) 46, program storage 48 such asROM or EEPROM, and data storage 50 such as a hard disk, all commonlyconnected to each other through a bus 53. The program storage 48 stores,among others, a treatment planning module 54 which includes a userinterface module that interacts with the user in planning for, executingand reviewing the result of a treatment. Any of the software programmodules in the program storage 48 and data from the data storage 50 canbe transferred to the memory 44 as needed and is executed by the CPU 46.

In one embodiment, the computer 40 is built into the voltage generator10. In another embodiment, the computer 40 is a separate unit which isconnected to the voltage generator through the communications link 52.In a preferred embodiment, the communication link 52 is a USB link. Inone embodiment, the imaging device 30 is a standalone device which isnot connected to the computer 40. In the embodiment as shown in FIG. 1,the computer 40 is connected to the imaging device 30 through acommunications link 53. As shown, the communication link 53 is a USBlink. In this embodiment, the computer can determine the size andorientation of the lesion 300 by analyzing the data such as the imagedata received from the imaging device 30, and the computer 40 candisplay this information on the monitor 11. In this embodiment, thelesion image generated by the imaging device 30 can be directlydisplayed on the grid (not shown) of the display device (monitor) 11 ofthe computer running the treatment planning module 54. This embodimentwould provide an accurate representation of the lesion image on thegrid, and may eliminate the step of manually inputting the dimensions ofthe lesion in order to create the lesion image on the grid. Thisembodiment would also be useful to provide an accurate representation ofthe lesion image if the lesion has an irregular shape.

It should be noted that the software can be used independently of thepulse generator 10. For example, the user can plan the treatment in adifferent computer as will be explained below and then save thetreatment parameters to an external memory device, such as a USB flashdrive (not shown). The data from the memory device relating to thetreatment parameters can then be downloaded into the computer 40 to beused with the generator 10 for treatment. Additionally, the software canbe used for hypothetical illustration of zones of ablation, temperaturethresholds or cutoffs, and electrical field thresholds or cutoffs fortraining purposes to the user on therapies that deliver electricalenergy. For example, the data can be evaluated by a human to determineor estimate favorable treatment protocols for a particular patientrather than programmed into a device for implementing the particularprotocol.

FIG. 3 illustrates one embodiment of a circuitry to detect anabnormality in the applied pulses such as a high current, low current,high voltage or low voltage condition. This circuitry is located withinthe generator 10 (see FIG. 1). A USB connection 52 carries instructionsfrom the user computer 40 to a controller 71. The controller can be acomputer similar to the computer 40 as shown in FIG. 2. The controller71 can include a processor, ASIC (application-specific integratedcircuit), microcontroller or wired logic. The controller 71 then sendsthe instructions to a pulse generation circuit 72. The pulse generationcircuit 72 generates the pulses and sends electrical energy to theprobes. For clarity, only one pair of probes/electrodes are shown.However, the generator 10 can accommodate any number ofprobes/electrodes (e.g., from 1-10, such as 6 probes) and energizingmultiple electrodes simultaneously for customizing the shape of theablation zone. In the embodiment shown, the pulses are applied one pairof electrodes at a time, and then switched to another pair. The pulsegeneration circuit 72 includes a switch, preferably an electronicswitch, that switches the probe pairs based on the instructions receivedfrom the computer 40. A sensor 73 such as a sensor can sense the currentor voltage between each pair of the probes in real time and communicatesuch information to the controller 71, which in turn, communicates theinformation to the computer 40. If the sensor 73 detects an abnormalcondition during treatment such as a high current or low currentcondition, then it will communicate with the controller 71 and thecomputer 40 which may cause the controller to send a signal to the pulsegeneration circuit 72 to discontinue the pulses for that particular pairof probes. The treatment planning module 54 can further include afeature that tracks the treatment progress and provides the user with anoption to automatically retreat for low or missing pulses, orover-current pulses (see discussion below). Also, if the generator stopsprematurely for any reason, the treatment planning module 54 can restartat the same point where it terminated, and administer the missingtreatment pulses as part of the same treatment. In other embodiments,the treatment planning module 54 is able to detect certain errors duringtreatment, which include, but are not limited to, “charge failure”,“hardware failure”, “high current failure”, and “low current failure”.

General treatment protocols for the destruction (ablation) ofundesirable tissue through electroporation are known. They involve theinsertion (bringing) electroporation electrodes to the vicinity of theundesirable tissue and in good electrical contact with the tissue andthe application of electrical pulses that cause irreversibleelectroporation of the cells throughout the entire area of theundesirable tissue. The cells whose membrane was irreversiblepermeabilized may be removed or left in situ (not removed) and as suchmay be gradually removed by the body's immune system. Cell death isproduced by inducing the electrical parameters of irreversibleelectroporation in the undesirable area.

Electroporation protocols involve the generation of electrical fields intissue and are affected by the Joule heating of the electrical pulses.When designing tissue electroporation protocols it is important todetermine the appropriate electrical parameters that will maximizetissue permeabilization without inducing deleterious thermal effects. Ithas been shown that substantial volumes of tissue can be electroporatedwith reversible electroporation without inducing damaging thermaleffects to cells and has quantified these volumes (Davalos, R. V., B.Rubinsky, and L. M. Mir, Theoretical analysis of the thermal effectsduring in vivo tissue electroporation. Bioelectrochemistry, 2003. Vol.61(1-2): p. 99-107).

The electrical pulses used to induce irreversible electroporation intissue are typically larger in magnitude and duration from theelectrical pulses required for reversible electroporation. Further, theduration and strength of the pulses for irreversible electroporation aredifferent from other methodologies using electrical pulses such as forintracellular electro-manipulation or thermal ablation. The methods arevery different even when the intracellular (nano-seconds)electro-manipulation is used to cause cell death, e.g. ablate the tissueof a tumor or when the thermal effects produce damage to cells causingcell death.

Typical values for pulse length for irreversible electroporation are ina range of from about 5 microseconds to about 62,000 milliseconds orabout 75 microseconds to about 20,000 milliseconds or about 100microseconds±10 microseconds. This is significantly longer than thepulse length generally used in intracellular (nano-seconds)electro-manipulation which is 1 microsecond or less—see published U.S.application 2002/0010491 published Jan. 24, 2002.

The pulse is typically administered at voltage of about 100 V/cm to7,000 V/cm or 200 V/cm to 2000 V/cm or 300V/cm to 1000 V/cm about 600V/cm for irreversible electroporation. This is substantially lower thanthat used for intracellular electro-manipulation which is about 10,000V/cm, see U.S. application 2002/0010491 published Jan. 24, 2002.

The voltage expressed above is the voltage gradient (voltage percentimeter). The electrodes may be different shapes and sizes and bepositioned at different distances from each other. The shape may becircular, oval, square, rectangular or irregular etc. The distance ofone electrode to another may be 0.5 to 10 cm, 1 to 5 cm, or 2-3 cm. Theelectrode may have a surface area of 0.1-5 sq. cm or 1-2 sq. cm.

The size, shape and distances of the electrodes can vary and such canchange the voltage and pulse duration used. Those skilled in the artwill adjust the parameters in accordance with this disclosure to obtainthe desired degree of electroporation and avoid thermal damage tosurrounding cells.

Additional features of protocols for electroporation therapy areprovided in U.S. Patent Application Publication No. US 2007/0043345 A1,the disclosure of which is hereby incorporated by reference in itsentirety.

In one aspect, the systems and methods may have the capability forestimating a volume of tissue that will be heated at or above a cutoffvalue and a volume of tissue that will receive an electric field at orabove a cutoff value for the above medical treatment device. The cut-offvalues may be user-specified values determined by a treating physicianor technician. The systems and methods are provided so that the treatingphysician may recognize treatments that produce overheating in thevicinity of the electrodes of the treatment device. This additionalcapability of the treatment device may be based on the Joule heatingequations of Example 8. The values may be plotted as contour lines whichmay be displayed with a graphical representation of the estimatedtreatment volume above. In one embodiment, the contour lines are Cassinioval approximations performed according to the equations and procedurein Example 7.

In another aspect, the systems and methods may have the additionalcapability for providing the electric field distributions usingdifferent configurations of bipolar probes and include the dynamicchange in electrical conductivity from the baseline non-electroporatedtissue. The systems and methods may allow a user to incorporatetissue-specific values for the dynamic change in conductivity inestimating a treatment volume. This additional capability is furtherdescribed in Example 9. In one embodiment, the contour lines are Cassinioval approximations performed according to the equations and procedurein Example 7.

In another aspect, the systems and methods may have the additionalcapability for inputting or adjusting one or more variables related tothe dynamic conductivity so that tissue-specific behavior can beaccounted for when estimating a treatment volume. In embodiments, thetreatment planning module may provide input for parameters such as thebaseline conductivity, change in conductivity, the transition zone (howrapidly the conductivity increases), the electric field at which thechange in conductivity occurs, and the electric field at whichirreversible electroporation occurs. These parameters may allow thetreating physician to fine-tune the ablation zone based on theconductivity characteristics of the target tissue. The present inventorshave recognized that the conductivity characteristics of the tissue,such as baseline and maximum conductivities, should be determined beforethe therapy in order to determine safe and effective pulse protocols.This additional capability is further described in Example 10.

The numerical models and algorithms of the invention, as provided in theExamples, such as Cassini Oval equations of Example 7 and the JouleHeating Model equations of Example 8, can be implemented in a system forestimating a 3-dimensional treatment volume for a medical treatmentdevice that applies treatment energy through one or more or a pluralityof electrodes defining a treatment area. In one embodiment, thenumerical models and algorithms are implemented in an appropriatecomputer readable code as part of the treatment planning module 54 ofthe system of the invention. Computing languages available to theskilled artisan for programming the treatment planning module 54 includegeneral purpose computing languages such as the C and related languages,and statistical programming languages such as the “S” family oflanguages, including R and S-Plus. The computer readable code may bestored in a memory 44 of the system of the invention. A processor 46 iscoupled to the memory 44 and a display device 11 and the treatmentplanning module 54 stored in the memory 44 is executable by theprocessor 46. Treatment planning module 54, through the implementednumerical models, is adapted to generate a graphical display of anestimated temperature or electric field or target ablation zone in thedisplay device 11.

In one embodiment, the invention provides for a system for estimatingand graphically displaying a thermal and/or electric field value for amedical treatment device that applies treatment energy through one ormore or a plurality of electrodes 22 defining a treatment area, thesystem comprising a memory 44, a display device 11, a processor 46coupled to the memory 44 and the display device 11, and a treatmentplanning module 54 stored in the memory 44 and executable by theprocessor 46, the treatment planning module 54 adapted to generate oneor more isocontours representing a value of a temperature and/orelectric field for display in the display device 11 based on modeling ofthe temperature distributions or electrical field distributionsaccording to one or more parameters defining an electrical energy basedprotocol (e.g., irreversible electroporation). The results of modelingthe temperature distributions and electrical field distributions may bestored in a database or calculated in real-time. The treatment planningmodule may generate the isocontours based on the modeling results.

In another embodiment, the invention provides for a system forestimating a target ablation zone for a medical treatment device thatapplies treatment energy through one or more or a plurality ofelectrodes 22 defining a treatment area, the system comprising a memory44, a display device 11, a processor 46 coupled to the memory 44 and thedisplay device 11, and a treatment planning module 54 stored in thememory 44 and executable by the processor 46, the treatment planningmodule 54 adapted to generate a target ablation zone in the displaydevice 11 based on a combination of one or more parameters for atreatment protocol for irreversible electroporation and one or moretissue-specific conductivity parameters.

The foregoing description provides additional instructions andalgorithms for a computer programmer to implement in computer readablecode a treatment planning module 54 that may be executable through aprocessor 46 to generate an estimated temperature or electrical fieldfor display in the display device 11 based on modeling of a tissueaccording to one or more parameters for electroporation, such as IRE.The computer readable code may also estimate a temperature value and anelectric field value according to equations described in Example 8 andgraphically display these value as contour lines in the display device.In one embodiment, the contour lines are Cassini oval approximationsperformed according to the equations and procedure in Example 7. Thecomputer readable code may also provide for input on one or moreconductivity parameters for estimating the target ablation zone asdescribed in Examples 9 and 10.

FIG. 4 is a schematic diagram showing a three-dimensional zone ofablation occurring during irreversible electroporation. The width anddepth of this zone of ablation may be modeled two-dimensionally usingthe Cassini oval equation. Further, the mathematical fit of the zone ofablation has similar shape characteristics as the actual and simulatedelectric field and temperature values. For example, a typical singlebi-polar probe will be configured to have a first and second electrodespaced apart from each other at the distal end of the single probe.Since the lesion formed by this bi-polar arrangement closely resemblesthe 8-like shape of the electric field, the method of the invention canbe used to accurately predict the electric field and temperaturecontours. FIGS. 16A and 16B show variations of ‘a’ and ‘b’ parametersthat will closely resemble the 8-like shape of the electric fieldaccording to the Cassini Equation.

The method of the invention fits data extracted from numericalsimulations to both the ‘a’ and ‘b’ parameters from the CassiniEquation, providing the flexibility to match potentially any shape ofelectric field created by the specific pulse parameters employed. Also,as illustrated in FIGS. 16A and 16B since the ‘a’ or ‘b’ parameters arenot related to the separation distance or geometry of the electrodes,the electric field and temperature contours of the bi-polar probe can becaptured according to the techniques described above.

Additionally, by adding the cumulative effects of electrode pairs, theelectric field and thermal contours of alternative multi-electrodearrangements of three or more probes can be determined. For example, afour single probe electrode box can be captured by calculating treatmentregions based on each combination of electrode pairs for the fitaccording to the techniques described above. Thus, for example, if thefour probe electrode box is configured for treatment using pulses thatcycle through probe combinations 1-2, 3-4, 1-3, 2-4, 2-3 and 1-4 theapproximation tool can find electric field and temperature contours foreach probe combination, then superimpose the results to display thecumulative effect of that particular pulse protocol in the treatmentregion.

In one embodiment, the treatment planning module 54 provides for amethod for modeling and graphical display of tissue heating according toa set of parameters defining a treatment protocol. In a specificembodiment, the set of parameters correspond to a treatment protocol forinducing irreversible electroporation in a tissue.

The treatment planning module 54 may provide one or more parameters of atreatment protocol for delivering one or more electrical pulses to atissue through one or more or a plurality of electrodes.

The treatment planning module 54 may model a heat distribution in atissue surrounding the one or more or the plurality of electrodes basedon the one or more parameters.

The treatment planning module 54 may provide a graphical representationof the heat distribution based on the modeled heat distribution.

The treatment planning module 54 may allow a user to optionally modifyone or more of the parameters of the treatment protocol through inputdevices 12, 14 based on the graphical representation of the heatdistribution.

The treatment planning module 54 may be in operable connection with acontroller 71 capable of delivering one or more electrical pulses to thetissue based on the one or more parameters stored in the treatmentplanning module 54.

The treatment planning module 54 may model the heat distribution in thetissue based on the Joule heating in the tissue.

The treatment planning module 54 may calculate the heat distribution as:

${\rho\; C_{p}\frac{\partial T}{\partial t}} = {{\nabla{\cdot \left( {k{\nabla T}} \right)}} + {Q_{j\; h}\left\lbrack \frac{W}{m^{3}} \right\rbrack}}$

where ρ is the density, C_(p) is the heat capacity, k is the thermalconductivity, and Q_(jh) are the resistive losses

$Q_{j\; h} = {J \cdot {E\left\lbrack \frac{W}{m^{3}} \right\rbrack}}$

where J is the induced current density

$J = {\sigma\;{E\left\lbrack \frac{A}{m^{2}} \right\rbrack}}$

and σ is the tissue conductivity and E is the electric field

$E = {- {\nabla{\phi\left\lbrack \frac{V}{m} \right\rbrack}}}$

The treatment planning module may further calculate the resistive lossesasjh·Qrh=((jh·Jix+jh·Jex)*duty_cycle*jh·Ex(jh·Jiy+jh·Jey)*duty_cycle*jh·Ey+(jh·Jiz+jh·Jez)*duty_cycle*jh·Ez)*(t<=90)+0*(t>90)according to the Joule Heating Model described in Example 8.

The treatment planning module 54 may allow a user to specify a heatdistribution value (i.e. temperature) and may provide a graphicalrepresentation of the temperature as an isocontour line.

The treatment planning module 54 may model an electric fielddistribution in a tissue surrounding the one or more or a plurality ofelectrodes based on the one or more parameters of the treatmentprotocol.

The treatment planning module 54 may provide a graphical representationof the electric field distribution based on the modeled electrical fielddistribution.

The treatment planning module may calculate the electric fielddistribution as:∇²ϕ=0

where ϕ is the electric potential, this equation is solved with boundaryconditions:

{right arrow over (n)}·{right arrow over (J)}=0 at the boundaries

ϕ=V_(in) at the boundary of the first electrode

ϕ=0 at the boundary of the second electrode

wherein {right arrow over (n)} is the normal vector to the surface,{right arrow over (J)} is the electrical current and V_(in) is theelectrical potential applied.

The treatment planning module 54 may allow a user to specify a value foran electrical field distribution and provide a graphical representationof the electrical field distribution value as an isocontour line.

The treatment planning module 54 may display isocontour linesrepresenting the heat and electrical field distributions by calculatinga Cassini oval according to Example 7. The Cassini oval may becalculated by first modeling the temperature and electrical fielddistributions, storing the values in a database, and then calculatingthe specific Cassini oval based on parameters chosen by the user.

The treatment planning module 54 may allow a user to specify the one ormore parameters of a treatment protocol including voltage, gap betweenelectrodes, duration, pulse width, and electric field intensity.

Alternatively, or in addition, the treatment planning module 54 mayallow a user to input one or more of the tissue-specific conductivityparameters described herein and model the electric field distributionand tissue heating. The treatment planning module 54 may then providegraphical representations of one or more values of the electrical fieldintensity and tissue temperature.

The treatment planning module 54 may provide a graphical representationof an electrical field distribution and a heat distribution through avariety of modes of operation. First, the treatment planning module 54may model the electrical field distribution and heat distribution foreach set of parameters that are entered through input devices 12, 14.Thus, every time the treating physician altered one or more parametersof the treatment protocol, the treatment planning module 54 softwarewould model the electrical field and heat distributions according tothose parameters and then graphically display them on the display device11. In a second approach, the software would first run the modeling ofthe heat and electrical field distributions for a wide range ofparameter combinations and store the resulting distributions in thedatabase stored in memory 44. In this approach, when the treatingphysician enters a particular combination of parameters, the treatmentplanning module 54 retrieves the heat distribution and electrical fielddistribution from values stored in the database. These values are thenused as a basis for Cassini oval calculations to determine specificcontours for the particular combination of parameters. The Cassini ovalcalculations are performed according to the equations and proceduredescribed in Example 7. The Cassini ovals are then graphically displayedon the display device 11 in real time. In embodiments, specific contoursare provided according to values for temperature or electrical fieldintensity set by the user.

The treatment planning module 54 may model the heat and electric fielddistributions according to mathematical formulas. In a specificembodiment, the treatment planning module 54 may model the heatdistribution and the electrical field distribution according to theformulas in Example 8.

In another embodiment, the invention provides a system for treating atissue, which system applies electrical treatment energy through one ormore or a plurality of electrodes defining a target treatment area ofthe tissue. The system comprises a computer 40 comprising: a memory 44,a display device 11, a processor 46 coupled to the memory 44 and thedisplay device 11; and a treatment planning module 54 stored in thememory 44 and executable by the processor 46. In this embodiment, thetreatment planning module 54 is adapted to: provide one or moreparameters of a treatment protocol for delivering one or more electricalpulses to a tissue through one or more or a plurality of electrodes;model a heat distribution in a tissue surrounding the at least electrodebased on the one or more parameters; provide a graphical representationof the heat distribution on the display device 11 based on the modeledheat distribution. The system further comprises input devices 12, 14 inoperable connection with computer 40, which input devices are capable ofmodifying the one or more parameters of the treatment protocol in thetreatment planning module 54. The system further comprises a generator10 in operable connection with the computer through a controller 71,which controller 71 is capable of instructing the generator 10 todeliver the one or more electrical pulses to the target tissue throughthe one or more or the plurality of electrodes 22 based on the one ormore parameters of the treatment protocol stored in the treatmentplanning module 54. The system may further comprise one or moredatabases stored in the memory 44 for storing the modeled heatdistributions or modeled electric field distributions for a plurality ofsets of parameters for a treatment protocol.

In another embodiment, the treatment planning module 54, in addition toproviding one or more parameters of a treatment protocol for deliveringone or more electrical pulses to a tissue through one or more or aplurality of electrodes, may also provide one or more conductivityparameters specific for the tissue to be treated.

The treatment planning module 54 may estimate the target ablation zonebased on the one or more parameters of the treatment protocol and theone or more electrical flow characteristics. The treatment planningmodule may also display a graphical representation of the estimation inthe display device 11.

The treatment planning module 54 may optionally allow for modificationof one or more of the parameters of the treatment protocol through inputdevices 12, 14 based on the graphical representation of the targetablation zone.

Additionally, the treatment planning module 54 may be in operablecommunication with a controller 77 and provide one or more parameters tothe controller for delivering one or more electrical pulses to thetissue.

The treatment planning module 54 may provide one or more parameters of atreatment protocol comprise voltage, gap between electrodes, duration,pulse width, and electric field intensity.

Additionally, the one or more conductivity parameters provided by thetreatment planning module 54 may comprise the baseline conductivity ofthe tissue to be treated, the ratio of the baseline conductivity to themaximum conductivity of the tissue that is reached during treatment, therate at which the conductivity increases from the baseline to themaximum conductivity, or the electric field at which the conductivitychanges during treatment.

Additionally, one or more conductivity parameters for a plurality oftissues may be provided in a database stored in memory 44.

In another embodiment, the invention provides a system for treating atissue, which system applies electrical treatment energy through one ormore or a plurality of electrodes 22 defining a target treatment area ofthe tissue. The system may comprise a computer 40 comprising a memory44, a display device 11, a processor 46 coupled to memory 44 and thedisplay device 11, and a treatment planning module 54 stored in thememory 44 and executable by the processor 46. The treatment planningmodule 54 may be adapted to provide one or more parameters of atreatment protocol for delivering one or more electrical pulses to atissue through one or more or a plurality of electrodes, provide one ormore conductivity parameters specific for the tissue to be treated,estimate the target ablation zone and display a graphical representationof the estimation in the display device based on the one or moreparameters of the treatment protocol and the one or more conductivityparameters. The system may further comprise input devices 12, 14 inoperable connection with the computer 40, which input devices 12, 14 arecapable of allowing a user to modify the one or more parameters of thetreatment protocol in the treatment planning module 54. The system mayfurther comprise a generator 10 in operable connection with the computer40 through a controller 71, which controller 71 is capable ofinstructing the generator 10 to deliver the one or more electricalpulses to a tissue through the one or more or the plurality ofelectrodes 22 based on the one or more parameters of the treatmentprotocol stored in the treatment planning module 54. Additionally, thesystem may comprise a database of conductivity parameters for aplurality of tissues stored in the memory 44.

The systems of the invention may be further configured to includesoftware for displaying a Graphical User Interface in the display devicewith various screens for input and display of information, includingthose for inputting various parameters or display of graphicalrepresentations of zones of temperature, electrical field, and ablation.Additionally, the Graphical User Interface (GUI) may allow a user toinput one or more values related to an irreversible electroporationprotocol and tissue-specific conductivity measurements through the useof text fields, check boxes, pull-downs, sliders, command buttons, tabs,and the like.

In one embodiment, the invention provides a method of treating a tissuewith a medical treatment device that applies electrical treatment energythrough one or more or a plurality of electrodes defining a targettreatment area of the tissue and that comprises a display device. Themethod may comprise providing one or more parameters of a treatmentprotocol for delivering one or more electrical pulses to a tissuethrough one or more or a plurality of electrodes, modeling a heatdistribution in a tissue surrounding the at least electrode based on theone or more parameters, displaying a graphical representation of theheat distribution based on the modeled heat distribution in the displaydevice, modifying one or more of the parameters of the treatmentprotocol based on the graphical representation of the heat distribution,and implanting one or a plurality of electrodes in the tissue anddelivering one or more electrical pulses to the tissue through theelectrodes based on the one or more modified parameters.

In an exemplary implementation of the method, a treating physicianidentifies a target treatment area in a tissue of a patient. Forexample, the target treatment area may be a tumor that is unresectableby conventional surgical methods. The treating physician then uses inputdevices 12, 14 such as a keyboard or mouse to interact with thetreatment planning module 54 to select and input one or more parametersfor designing an irreversible electroporation treatment protocol forablating the tumor. The treating physician then selects a temperaturevalue to graphically display a temperature contour profile in the targettreatment area on the display device 11. For example, the treatingphysician may select a value of 50° C. The treating physician then maycorrelate this temperature contour with imaging from the treatment area,by overlaying the temperature contour with the imaging on the displaydevice 11. By visualizing the temperature contour relative to theimaging, the treating physician then may identify structures surroundingthe treatment area such as nerves and blood vessels that may be subjectto thermal damage. The treating physician then may modify theirreversible electroporation parameters so that the temperature contourno longer indicates that critical structures may be subject tooverheating. Irreversible electroporation parameters that may bemodified include the voltage, distance between electrodes, electrodediameter, period of treatment, pulse width, number of pulses, andelectric field. Similarly, the treatment planning module 54 may allowthe treating physician to visualize a temperature contour relative to anelectric field contour. Through one or more iterations of adjustment ofthe irreversible electroporation parameters and visualization of thetemperature contour and electric field contour on the display device,the treating physician may ultimately select a final set of irreversibleelectroporation parameters to be used for treatment. The treatingphysician may then implant a pair of electrodes at the target treatmentarea in the tissue and deliver a plurality of electrical pulses to thetreatment area based on the final set of irreversible electroporationparameters.

Thus, one embodiment of the method may comprise one or more of: 1.identifying a target treatment area in a tissue of a patient; 2.selecting and inputting one or more parameters for designing anirreversible electroporation treatment protocol for the target treatmentarea; 3. selecting a temperature value to graphically display atemperature contour in a simulation of the target treatment area; 4.correlating the temperature contour with imaging from the treatmentarea; 5. Identifying structures within or surrounding the targettreatment area such as nerves and blood vessels that may be subject tothermal damage based on the temperature contour; 6. modifying theirreversible electroporation parameters through one or more iterationsso that the temperature contour no longer indicates that criticalstructures may be subject to overheating; 7. selecting a final set ofirreversible electroporation parameters to be used for treatment; and 8.implanting a pair of electrodes at the target treatment area in thetissue and delivering a plurality of electrical pulses to the treatmentarea based on the final set of irreversible electroporation parameters.

The target treatment area may be imaged through a variety of imagingmodalities including Computed Tomography (CT), Magnetic ResonanceImaging (MRI), Ultrasound, Positron Emission Tomography (PET), and thelike. The imaging devices may be operably connected with the displaydevice 11 so that results of the imaging may overlap or otherwise beavailable for comparison with the graphical display of the temperatureand electric field contours.

In another embodiment, the invention provides a method of treating atissue with a medical treatment device that applies electrical treatmentenergy through one or more or a plurality of electrodes defining atarget treatment area of the tissue, which medical treatment devicecomprises a display device. The method may comprise providing one ormore parameters of a treatment protocol for delivering one or moreelectrical pulses to a tissue through one or a plurality of electrodes,and one or more conductivity parameters specific for the tissue to betreated, estimating the target ablation zone and displaying a graphicalrepresentation of the estimation in the display device based on the oneor more parameters of the treatment protocol and the one or moreconductivity parameters, modifying one or more of the parameters of thetreatment protocol based on the graphical representation of the targetablation zone, and implanting one or a plurality of electrodes in thetissue and delivering one or more electrical pulses to the tissuethrough the electrodes based on the one or more modified parameters. Inthe context of this specification, when referring to implanting anelectrode, one or more of the electrode(s) can alternatively or inaddition be placed near, or contact, or otherwise be operably disposedin a manner to administer electrical energy to the tissue.

In an exemplary implementation of the method, a treating physicianidentifies a target treatment area in a tissue of a patient. Forexample, the target treatment area may be a tumor that is unresectableby conventional surgical methods. The treating physician then uses inputdevices 12, 14 such as a keyboard or mouse to interact with thetreatment planning module 54 to select and input one or more parametersfor designing an irreversible electroporation treatment protocol forablating the tumor. The treatment planning module 54 then graphicallydisplays an ablation zone on the display device 11 based on the one ormore parameters of the irreversible electroporation treatment protocol.The treating physician then selects one or more conductivity parametersbased on the type of tissue to be treated. The one or more conductivityparameters may be tissue-specific values based on experimental data thatis stored in a database in memory 44 or may be obtained by the physicianand entered into the treatment planning module 54 using the keyboard orother input, such as a hands-free input. In embodiments, tissue-specificconductivity values may be provided for heart, kidney, liver, lung,spleen, pancreas, brain, prostrate, breast, small intestine, largeintestine, and stomach.

The one or more conductivity parameters may include the baselineconductivity, change in conductivity, the transition zone (how rapidlythe conductivity increases), the electric field at which the change inconductivity occurs, and the electric field at which irreversibleelectroporation occurs. After selecting the one or more conductivityparameters, the treatment planning module 54 may display a modifiedablation zone on the display device 11 based on the tissue-specificconductivity characteristics inputted by the physician. The treatingphysician then may alter the one or more parameters of the irreversibleelectroporation protocol to modify the target ablation zone on thedisplay device 11 to fit a desired area of treatment. The treatingphysician may then strategically place (e.g., implant) a pair ofelectrodes at the target treatment area in the tissue and deliver aplurality of electrical pulses to the treatment area based on the finalset of irreversible electroporation parameters.

Thus, one embodiment of the method may comprise one or more of: 1.identifying a target treatment area in a tissue of a patient; 2.selecting and inputting one or more parameters for designing anirreversible electroporation treatment protocol for the target treatmentarea; 3. displaying a graphical representation of a target ablation zoneon a display device; 4. selecting and inputting one or more conductivitycharacteristics based on the specific tissue to be treated; 5.displaying a modified graphical representation of the target ablationzone based on the tissue-specific conductivity characteristics; 6.modifying the one or more parameters of the irreversible electroporationprotocol to fit a desired area of treatment; and 7. disposing/implantinga pair of electrodes at the target treatment area in the tissue anddelivering a plurality of electrical pulses to the treatment area basedon the modified IRE parameters.

As will be apparent to a skilled artisan, the systems and methodsdescribed above may be compatible with a variety of bi-polar andmono-polar probe combinations and configurations. Additionally, thecalculations may be extended to not only display an electric field andtemperature but also using that information to calculate an electricaldamage and thermal damage component which take into account the time ofexposure to the electric field and temperatures and can betissue-specific such as for liver, kidney, etc. The systems and methodsmay be capable of displaying information such as “electric damage” or“thermal damage” once the electric field and temperature contours aredetermined, based on predetermined values for electric damage andthermal damage in the given tissue type. “Electric damage” and “thermaldamage” regions can be visualized in place of or in combination withelectric field and temperature as isocontour lines, shaded orhighlighted areas, or other forms of graphical representation. Inaddition, the inclusion of tissue-specific in-vivo derived dataincluding blood flow, metabolic heat generation, and one or moreconductivity parameters such as tissue conductivity and ratios ofchanging conductivity can be included to reflect dynamic changes withina specific tissue type.

Additional details of the algorithms and numerical models disclosedherein will be provided in the following Examples, which are intended tofurther illustrate rather than limit the invention.

In Example 1, the present inventors provide a numerical model that usesan asymmetrical Gompertz function to describe the response of porcinerenal tissue to electroporation pulses. However, other functions couldbe used to represent the electrical response of tissue under exposure topulsed electric fields such as a sigmoid function, ramp, and/orinterpolation table. This model can be used to determine baselineconductivity of tissue based on any combination of electrode exposurelength, separation distance, and non-electroporating electric pulses. Inaddition, the model can be scaled to the baseline conductivity and usedto determine the maximum electric conductivity after theelectroporation-based treatment. By determining the ratio ofconductivities pre- and post-treatment, it is possible to predict theshape of the electric field distribution and thus the treatment volumebased on electrical measurements. An advantage of this numerical modelis that it is easy to implement in computer software code in the systemof the invention and no additional electronics or numerical simulationsare needed to determine the electric conductivities. The system andmethod of the invention can also be adapted for other electrodegeometries (sharp electrodes, bipolar probes), electrode diameter, andother tissues/tumors once their response to different electric fieldshas been fully characterized.

The present inventors provide further details of this numerical modelingas well as experiments that confirm this numerical modeling in Example2. In developing this work, the present inventors were motivated todevelop an IRE treatment planning method and system that accounts forreal-time voltage/current measurements. As a result of this work, thesystem and method of the invention requires no electronics or electrodesin addition to the NANOKNIFE® System, a commercial embodiment of asystem for electroporation-based therapies. The work shown in Example 2is based on parametric study using blunt tip electrodes, but can becustomized to any other geometry (sharp, plate, bipolar). The numericalmodeling in Example 2 provides the ability to determine a baselinetissue conductivity based on a low voltage pre-IRE pulse(non-electroporating ˜50 V/cm), as well as the maximum tissueconductivity based on high voltage IRE pulses (during electroporation)and low voltage post-IRE pulse (non-electroporating ˜50 V/cm). Twonumerical models were developed that examined 720 or 1440 parametercombinations. Results on IRE lesion were based on in vitro measurements.A major finding of the modeling in Example 2 is that the electric fielddistribution depends on conductivity ratio pre- and post-IRE.Experimental and clinical IRE studies may be used to determine thisratio. As a result, one can determine e-field thresholds for tissue andtumor based on measurements. The 3-D model of Example 2 captures depth,width, and height e-field distributions.

In Example 3, as a further extension of the inventors work, theinventors show prediction of IRE treatment volume based on 1000 V/cm,750 v/cm, and 500 V/cm IRE thresholds as well as other factors as arepresentative case of the numerical modeling of the invention.

In Example 4, the inventors describe features of the SpecificConductivity and procedures for implementing it in the invention.

In Example 5, the inventors describe in vivo experiments as a reductionto practice of the invention.

In Example 6, the inventors describe how to use the ratio of maximumconductivity to baseline conductivity in modifying the electric fielddistribution and thus the Cassini oval equation.

In Example 7, the inventors describe the Cassini oval equation and itsimplementation in the invention.

In Example 8, the inventors describe mapping of electric field andthermal contours using a simplified data cross-referencing approach.

In Example 9, the inventors describe visualization of electric fielddistributions using different configurations of bipolar probes.

In Example 10, the inventors describe a method for determining the IREthreshold for different tissues according to one or more conductivityparameters.

In Example 11, the inventors describe correlating experimental andnumerical IRE lesions using the bipolar probe.

EXAMPLES Example 1 Materials and Methods

The tissue was modeled as a 10-cm diameter spherical domain using afinite element package (Comsol 4.2a, Stockholm, Sweden). Electrodes weremodeled as two 1.0-mm diameter blunt tip needles with exposure lengths(Y) and edge-to-edge separation distances (X) given in Table 1. Theelectrode domains were subtracted from the tissue domain, effectivelymodeling the electrodes as boundary conditions.

TABLE 1 Electrode configuration and relevant electroporation-basedtreatment values used in study. PARAMETER VALUES MEAN W [V/cm] 500,1000, 1500, 2000, 1750 2500, 3000 X [cm] 0.5, 1.0, 1.5, 2.0, 2.5 1.5 Y[cm] 0.5, 1.0, 1.5, 2.0, 2.5, 3.0 1.75 Z [cm] 1.0, 1.25, 1.5, 2.0, 3.0,4.0, 2.968 5.0, 6.0 75

The electric field distribution associated with the applied pulse isgiven by solving the Laplace equation:∇·(σ(|E|)∇φ)=0  (1)

where σ is the electrical conductivity of the tissue, E is the electricfield in V/cm, and φ is the electrical potential (Edd and Davalos,2007). Boundaries along the tissue in contact with the energizedelectrode were defined as φ=V_(o), and boundaries at the interface ofthe other electrode were set to ground. The applied voltages weremanipulated to ensure that the voltage-to-distance ratios (VV)corresponded to those in Table 1. The remaining boundaries were treatedas electrically insulating, ∂φ/∂n=0.

The analyzed domain extends far enough from the area of interest (i.e.the area near the electrodes) that the electrically insulatingboundaries at the edges of the domain do not significantly influence theresults in the treatment zone. The physics-controlled finer mesh with˜100,000 elements was used. The numerical models have been adapted toaccount for a dynamic tissue conductivity that occurs as a result ofelectroporation, which is described by an asymmetrical Gompertz curvefor renal porcine tissue (Neal et al., 2012):σ(|E|)=σ_(o)+(σ_(max)−σ_(o))exp[−A·exp[−B·E]  (2)

where σ_(o) is the non-electroporated tissue conductivity and σ_(max) isthe maximum conductivity for thoroughly permeabilized cells, A and B arecoefficients for the displacement and growth rate of the curve,respectively. Here, it is assumed that σ_(o)=0.1 S/m but this value canbe scaled by a factor to match any other non-electroporated tissueconductivity or material as determined by a pre-treatment pulse. In thiswork the effect of the ratio of maximum conductivity to baselineconductivity in the resulting electric current was examined using the50-μs pulse parameters (A=3.05271; B=0.00233) reported by Neal et al.(Neal et. al., 2012). The asymmetrical Gompertz function showing thetissue electric conductivity as a function of electric field is, forexample, shown in FIG. 5.

The current density was integrated over the surface of the groundelectrode to determine the total current delivered. A regressionanalysis on the resulting current was performed to determine the effectof the parameters investigated and their interactions using theNonlinearModelFit function in Wolfram Mathematica 8.0. Current data fromthe numerical simulations were fit to a mathematical expression thataccounted for all possible interactions between the parameters:I=factor·[aW+bX+cY+dZ+e(W−W )(X−X )+f(W−W )(Y−Y )+g(W−W )(Z−Z )+h(X−X)(Y−Y )+i(X−X )(Z−Z )+j(Y−Y )(Z−Z )+k(W−W )(X−X )(Y−Y )+l(X−X )(Y−Y)(Z−Z )+m(W−W )(Y−Y )(Z−Z )+n(W−W )(X−X )(Z−Z )+o(W−W )(X−X )(Y−Y )(Z−Z)+p]  (3)

where I is the current in amps, W is the voltage-to-distance ratio[V/cm], X is the edge-to-edge distance [cm], Y is the exposure length[cm], and Z is the unitless ratio σ_(max)/σ_(o). The W, X, Y, and Z aremeans for each of their corresponding parameters (Table 1) and thecoefficients (a, b, c, . . . , n, o, p) were determined from theregression analysis (Table 2).

Results.

A method to determine electric conductivity change following treatmentbased on current measurements and electrode configuration is provided.The best-fit statistical (numerical) model between the W, X, Y, and Zparameters resulted in Eqn. 3 with the coefficients in Table 2(R²=0.999646). Every coefficient and their interactions had statisticalsignificant effects on the resulting current (P<0.0001*). With thisequation one can predict the current for any combination of the W, Y, X,Z parameters studied within their ranges (500 V/cm≤W≤3000 V/cm, 0.5cm≤X≤2.5 cm, 0.5 cm≤Y≤3.0 cm, and 1.0≤Z≤6.0). Additionally, by using thelinear results (Z=1), the baseline tissue conductivity can beextrapolated for any blunt-tip electrode configuration by delivering andmeasuring the current of a non-electroporating pre-treatment pulse. Thetechniques described in this specification could also be used todetermine the conductivity of other materials, such as non-biologicalmaterials, or phantoms.

TABLE 2 Coefficients (P < 0.0001*) from the Least Square analysis usingthe NonlinearModelFit function in Mathematica. ESTIMATE a → 0.00820 b →7.18533 c → 5.80997 d → 3.73939 e → 0.00459 f → 0.00390 g → 0.00271 h →3.05537 i → 2.18763 j → 1.73269 k → 0.00201 l → 0.92272 m → 0.00129 n →0.00152 o → 0.00067 p → −33.92640

FIG. 6 shows a representative case in which the effect of the W and Zare studied for electroporation-based therapies with 2.0 cm electrodesseparated by 1.5 cm. The 3D plot corroborates the quality of the modelwhich shows every data point from the numerical simulation (greenspheres) being intersected by the best-fit statistical (numerical)model. This 3D plot also shows that when Z is kept constant, the currentincreases linearly with the voltage-to-distance ratio (W). Similarly,the current increases linearly with Z when the voltage-to-distance ratiois constant. However, for all the other scenarios there is a non-linearresponse in the current that becomes more drastic with simultaneousincreases in Wand Z

In order to fully understand the predictive capability of thestatistical (numerical) model, two cases in which the current ispresented as a function of the exposure length and electrode separationare provided. FIG. 7A shows the linear case (Z=1) in which the currentcan be scaled to predict any other combination of pulse parameters aslong as the pulses do not achieve electroporation. For example, one candeliver a non-electroporation pulse (˜50 V/cm) and measure current. Thecurrent can then be scaled to match one of the W values investigated inthis study. By using Eqn. 3 and solving for the factor, the baselineelectric conductivity of the tissue can be determined and used fortreatment planning. FIG. 7B is the case in which the maximum electricconductivity was 0.4 S/m (Z=4) after electroporation. The trends aresimilar to the ones described in FIG. 5 in that if exposure length isconstant, the current increases linearly with increasing electrodeseparation and vice versa. However, even though the conductivity withinthe treated region increases by a factor of 4, the current increasesnon-linearly only by a factor of 3. This can be seen by comparing thecontours in FIG. 7A with those in FIG. 7B which consistently show thatthe curves are increased by a factor of 3.

Example 2 Determining the Relationship between Blunt Tip ElectrodeConfiguration and Resulting Current after IRE Treatment

Model Assumptions:

Gompertz Conductivity: Pulse duration=50 μs, Ex-vivo kidney tissue

Baseline Conductivity: σ=0.1 S/m

Spherical Domain: diameter=10 cm

Applied Voltage: Voltage=1000 V

Parametric Study:

Total Combinations: 720 models

Maximum Conductivity: 1.0×, 1.25×, 1.5×, 2×, 3×, 4×, 5×, 6× the baseline

Edge-to-edge Distance: 5, 10, 15, 20, 25 mm

Electrode Exposure: 5, 10, 15, 20, 25, 30 mm

Electrode Radius: 0.5, 0.75, 1.0 mm

The output of statistical analysis software (JMP 9.0) used to fit modeland determine the coefficients for all parameter combinations is shownin the tables of FIGS. 8A and 8B and the plot of FIG. 8C.

Parameters of Best Fit for Dynamic Conductivity Changes between 1×-6×the Baseline Conductivity (R²=0.96):

a=−1.428057; (*Intercept Estimate*)

b=−0.168944; (*Gap Estimate*)

c=2.1250608; (*Radius Estimate*)

d=0.2101464; (*Exposure Estimate*)

e=1.1114726; (*Factor Estimate*)

f=−0.115352; (*Gap-Radius Estimate*)

g=−0.010131; (*Gap-Exposure Estimate*)

h=−0.067208; (*Gap-Factor*)

i=0.0822932; (*Radius-Exposure Estimate*)

j=0.4364513; (*Radius-Factor Estimate*)

k=0.0493234; (*Exposure-Factor Estimate*)

l=−0.006104; (*Gap-Radius-Exposure Estimate*)

m=0.0165237; (*Radius-Exposure-Factor Estimate*)*)

n=−0.003861; (*Gap-Exposure-Factor Estimate*)

o=−0.041303; (*Gap-Radius-Factor Estimate*)

p=−0.002042; (*Gap-Radius-Exposure-Factor Estimate*)

Analytical Function for Dynamic Conductivity Changes Between 1×-6× theBaseline Conductivity (R²=0.96):

5 mm<gap=x<25 mm, 0.5 mm<radius=y<1.0 mm,

5 mm<exposure=z<30 mm, 1<factor=w<6

Default conductivity of 0.1 S/m and 1000 V which can be scaled fordynamic conductivities. The function is a linear combination of alliterations examined in the parametric study:Current(w,x,y,z)=a+bx+cy+dz+ew+f(x+bb)(y+cc)+g(x+bb)(z+dd)+h(x+bb)(w+ee)+i(y+cc)(z+dd)+j(y+cc)(w+ee)+k(z+dd)(w+ee)+l(x+bb)(y+cc)+m(y+cc)(z+dd)(w+ee)+n(x+bb)(z+dd)(w+ee)+o(x+bb)(y+cc)(w+ee)+p(x+bb)(y+cc)(z+dd)(w+ee)

FIGS. 9A-9E show the representative (15 mm gap) correlation betweencurrent vs. exposure length and electrode radius for maximumconductivities (1×-6×, respectively).

FIGS. 10A and 10B are tables showing experimental validation of the codefor determining the tissue/potato dynamic conductivity from in vitromeasurements.

Determining the Relationship Between Blunt Tip Electrode Configurationand e-Field Distribution after IRE Treatment

Model Assumptions:

Gompertz Conductivity: Pulse duration=50 μs, Ex-vivo kidney tissue

Baseline Conductivity: σ=0.1 S/m

Spherical Domain: diameter=10 cm

Electrode Radius: r=0.5 mm

Parametric Study:

Total Combinations: 1440 models

Maximum Conductivity: 1.0×, 1.25×, 1.5×, 2×, 3×, 4×, 5×, 6× the baseline

Edge-to-edge Distance: 5, 10, 15, 20, 25 mm

Electrode Exposure: 5, 10, 15, 20, 25, 30 mm

Voltage-to-distance Ratio: 500, 1000, 1500, 2000, 2500, 3000 V/cm

Example 3

Comparison of analytical solutions with statistical (numerical) model tocalculate current and explanation of procedure that results in 3D IREvolume.

The process of backing-out the electrical conductivity using theanalytical solutions and the one proposed in the “Towards a PredictiveModel of Electroporation-Based Therapies using Pre-Pulse ElectricalMeasurements” abstract presented in the IEEE Engineering in Medicine andBiology Conference in Aug. 28, 2012 in San Diego, Calif. were compared.A method to determine the predictive power of the equations to calculatecurrent is analyzing the residuals of the 1440 combinations ofparameters examined. In the context of this specification, a residual isthe difference between the predicted current and the actual current. Ascan be seen in FIGS. 11A and 11B with increasing non-linear change inconductivity due to electroporation and increasing applied electricfield there is an increase in the residual for both cases. The mainmessage though is that using the shape factor (analytical) method themaximum residual is 11.3502 A and with the statistical (numerical) modelthe maximum is 1.55583 A. This analysis suggests that the shape factormethod may be inadequate to predict the non-linear changes in currentthat occur during electroporation and for reliable predictions thestatistical (numerical) method may be better.

In terms of the prediction of the volume treated a representative methodis to map out the electric field 5 cm in the directions along the(x,0,0), (0,y,0), and (0,0,z) axes from the origin. In addition, theelectric field can be extracted along a line that starts at the originand ends at 3 cm along each of the axes. These plots contain theinformation for determining the distances at which a particular IREthreshold occurs. In embodiments, 1440 different parameter combinationswere simulated that resulted in data sets of 28,692 (x-direction),20,538 (y-direction), 27,306 (z-direction), and 25,116 (xyz-direction)for homogeneous conductivity. Even though these simulations only includedynamic conductivity changes due to electroporation, it is believed thatan identical analysis for simulations that also include the changes inconductivity due to temperature could also be performed. In this manner,it would be possible to determine irreversible electroporationthresholds as a function of temperature and electroporation.Manipulating these large data sets is challenging but it provides allthe necessary information to study the effect of electrode separation,electrode length, dynamic conductivity factor, and voltage-to-distanceratio for any position along the described paths. In order to be able tomanipulate the data and extract the distance for different IREthresholds, the function NonlinearModelFit (Mathematica) was used inorder to come up with analytical expressions that would closely matchthe electric field. A different function was used for each of thedirections studied in the positive directions along the Cartesiancoordinate system. The Micheilis Menten function was used along thex-direction (R²=0.978978), the analytical solution to the Laplaceequation along the y-direction (R²=0.993262), and the Logistic equationin the z-direction (R²=0.983204). Each of those functions was scaled bya 3rd order polynomial function that enabled the fit to incorporate theelectrode separation and electrode exposure as well. Even though thedescribed functions were used to fit the data from the numerical data,there might be other functions that are also appropriate and this willbe explored further in order to use the most reliable fit. In FIGS.12A-12C provided are representative contour plots of the electric fieldstrength at 1.0 cm from the origin using an edge-to-edgevoltage-to-distance ratio of 1500 V/cm assuming a z=1 which is the casefor non-electroporated electrical conductivity. It is important to notethat in this case the y and z data are starting from (0, 0, 0) and thex-data starts outside the external electrode-tissue boundary. Onerepresentative case is presented, but any of the 1440 parameterscombinations that were disclosed in the conference proceeding could beplotted as well.

The following functions describe the electric field [V/cm] distributionsalong the x-axis (E_(x)), y-axis (E_(y)), and z-axis (E_(z)) as afunction of voltage-to-distance (W), edge-to-edge separation between theelectrodes (X), exposure length (Y), maximum conductivity to baselineconductivity (Z), and distance in the x-direction (xx), y-direction(yy), and z-direction (zz).E _(x)(W,X,Y,Z,xx)=W*(a*Exp[−b·xx]+c)*(dX ³ +eX ² +fX+gY ³ +hY ²+iY+j)+k  Micheilis Menten Equation (electric field in the x-direction)

The coefficients for the NonlinearModelFit are given below:

a=−0.447392, b=8.98279, c=−0.0156167, d=−0.0654974, e=0.468234,f=−6.17716, g=0.326307, h=−2.33953, I=5.90586, j=−4.83018, k −9.44083

Laplace Equation (Electric Field in the y-Direction)

${E_{y}\left( {W,X,Y,Z,{y\; y}} \right)} = {a + {\left( {X^{3} + X^{2} + {b\; X} + {c\; Y^{3}} + {d\; Y^{2}} + {e\; Y} + f} \right)*\left( {h + {\frac{\left( {g\; W\; X\; Z} \right)}{2}*\left( \frac{1}{\left. {{Log}\left\lbrack \frac{X + 0.1}{0.05} \right\rbrack} \right)*} \right)*{{Abs}\left\lbrack {\frac{1}{{{\cdot y}\; y} - \frac{X}{2} - 0.05} - \frac{1}{{{\cdot y}\; y} + \frac{X}{2} + 0.05}} \right\rbrack}}} \right)}}$

The coefficients for the NonlinearModelFit are given below:

a=−56.6597, b=−42.9322, c=6.66389, d=−50.8391, e=141.263, f=138.934,g=0.00417123, h=0.184109

Logistic Equation (electric field in the z-direction)

${E_{z}\left( {W,X,Y,Z,{z\; z}} \right)} = {a + {\frac{b\; W\; Z}{1 + {c \cdot {{Exp}\left\lbrack {d \cdot \left( {\frac{2z\; z}{y} - e} \right)} \right\rbrack}}} \cdot \left( {{f\; X^{3}} + {g\; X^{2}} + {h\; X} + i} \right) \cdot \left( {{j\; Y^{3}} + {k\; Y^{2}} + {l\; Y} + m} \right)}}$

The coefficients for the NonlinearModelFit are given below:

a=49.0995, b=−0.00309563, c=1.39341, d=4.02546, e=1.24714, f=0.276404,g=−1.84076, h=4.93473, I=−9.13219, j=0.699588, k=−5.0242, l=12.8624,m=19.9113.

In order to visualize the predicted IRE shape the equation of anellipsoid was used and the semi-axes were forced to intersect with thelocations at which the IRE threshold wants to be examined. Therefore,the provided functions can be adjusted in real-time to display the IREvolume for any electric field threshold. This is important sincedifferent tissues have different IRE thresholds that depend on thetemperature, dielectric properties of the tissue, the electrodeconfiguration, and the pulse parameters used. Once again, even thoughthe equation for an ellipsoid is used to represent the IRE volume, otherfunctions may be evaluated that may also be appropriate to replicate themorphology of the zones of ablation being achieved experimentally suchas the Cassini curve. A 1500 V/cm was used as the voltage-to-distanceratio, electrode exposure 2 cm, and electrode separation 1.5 cm togenerate 3 different IRE zones using 1000 V/cm, 750 V/cm, and 500 V/cmas the IRE thresholds with z=1.

From the 3D plots representing the zones of ablation shown in FIGS.13A-13C it can be seen that if the IRE threshold is reduced from 1000V/cm to either 750 V/cm or 500 V/cm, the volume becomes larger. This isrepresentative of how different tissues may have different thresholdsand this code may provide the ability to simulate the fields in abroad/generic manner that can then be applied to any tissue.Incorporating the xyz-data that was extracted from the parametric studywill help modify the “roundness” of the current depictions of the zoneof IRE ablation in order to more realistically replicate theexperimental results. However, to the best of the inventors' knowledgethere is no such adaptable code currently available to provide a 3D IREvolume as a function of measured current, electrode length, electrodeexposure, applied voltage-to-distance ratio, and customizable electricfield threshold so it is believed that this will greatly help themedical community in planning and verifying the clinical treatments ofpatients being treated with the IRE technology.

Example 4 Specific Conductivity

Specific conductivity can be important in embodiments for treatmentplanning of irreversible electroporation (IRE). For many applications,especially when treating tumors in the brain, the volume (area) of IREshould be predicted to maximize the ablation of the tumorous tissuewhile minimizing the damage to surrounding healthy tissue. The specificelectrical conductivity of tissue during an irreversible electroporation(IRE) procedure allows the physicians to: determine the currentthreshold; minimize the electric current dose; decrease the Jouleheating; and reduce damage to surrounding healthy tissue. To measure thespecific conductivity of tissue prior to an IRE procedure the physiciantypically performs one or more of the following: establishes theelectrode geometry (shape factor); determines the physical dimensions ofthe tissue; applies a small excitation AC voltage signal (1 to 10 mV);measures the AC current response; calculates the specific conductivity(σ) using results from the prior steps. This procedure tends to notgenerate tissue damage (low amplitude AC signals) and will supply thephysician (software) with the required information to optimize IREtreatment planning, especially in sensitive organs like the brain whichis susceptible to high electrical currents and temperatures. Thus, theIRE procedure is well monitored and can also serve as a feedback systemin between series of pulses and even after the treatment to evaluate thearea of ablation.

Special Cases for electrode geometry

Nomenclature (units in brackets):

V_(e)=voltage on the hot electrode (the highest voltage), [V]

G=electroporation voltage gradient (required for electroporation), [V/m]

R₁=radius of electrode with highest voltage (inner radius), [m]

R₂=radius at which the outer electrodes are arranged (outer radius), [m]

i=total current, [A]

L=length of cylindrical electrode, [m]

A=area of plate electrode, [m²]

σ=electrical conductivity of tissue, [S/m]

ρ=density

c=heat capacity

Case 1

Electrical conduction between a two-cylinder (needle) arrangement oflength L in an infinite medium (tissue). It is important to note thatthis formulation is most accurate when L>>R₁,R₂ and L>>w. The electricalconductivity can be calculated from,

$\sigma = \frac{i \cdot S}{V_{e}}$

where the shape factor (S) corresponding to the electrode dimensions andconfiguration is given by,

$\frac{2 \cdot \pi \cdot L}{\cosh^{- 1}\left( \frac{{4 \cdot w^{2}} - \left( {2 \cdot R_{1}} \right)^{2} - \left( {2 \cdot R_{2}} \right)^{2}}{8 \cdot R_{1} \cdot R_{2}} \right)}$

Case 2

Cylindrical arrangement in which the central electrode is a cylinder(needle) with radius R₁ and the outer electrodes are arranged in acylindrical shell with a shell radius of R₂ (not the radius of theelectrodes). The voltage on the central electrode is V_(e). The voltagedistribution in the tissue may be determined as a function of radius, r:

$V = {V_{e}\frac{\ln\frac{r}{R_{2}}}{\ln\frac{R_{1}}{R_{2}}}}$

The required voltage on the central electrode to achieve IRE:

$V_{e} = {G\; R_{2}\ln\frac{R_{2}}{R_{1}}}$

The required current on the central electrode:

$i = \frac{2\;\pi\; L\;\sigma\; V_{e}}{\ln\frac{R_{2}}{R_{1}}}$

The specific conductivity (σ) of the tissue can be calculated since thevoltage signal (V_(e)) and the current responses (i) are known.

Explanation of Electrical Concepts.

By using the bipolar electrode described previously in US PatentApplication Publication No. 2010/0030211A1, one can apply a smallexcitation AC voltage signal (for example from about 1 to 10 mV),V(t)=V ₀ Sin(ωt)

where V(t) is the potential at time t, V₀ is the amplitude of theexcitation signal and ω is the frequency in radians/s. The reason forusing a small excitation signal is to get a response that ispseudo-linear since in this manner the value for the impedance can bedetermined indicating the ability of a system (tissue) to resist theflow of electrical current. The measured AC current (response) that isgenerated by the excitation signal is described byI(t)=I ₀ Sin(ωt+θ)

where I(t) is the response signal, I₀ is the amplitude of the response(I₀≠V₀) and θ is the phase shift of the signal. The impedance (Z) of thesystem (tissue) is described by,Z=(V(t))/(I(t))=(V ₀ Sin(ωt))/(I ₀ Sin(ωt+θ))=Z ₀(Sin(ωt)/(Sin(ωt+θ))

It is important to note that the measurement of the response is at thesame excitation frequency as the AC voltage signal to preventinterfering signals that could compromise the results. The magnitude ofthe impedance |Z₀| is the electrical resistance of the tissue. Theelectrical resistivity (Ωm) can be determined from the resistance andthe physical dimensions of the tissue in addition to the electrodegeometry (shape factor). The reciprocal of the electrical resistivity isthe electrical conductivity (S/m). Therefore, after deriving theelectrical resistivity from the methods described above, theconductivity may be determined.

As described in U.S. Patent Application No. 61/694,144 the analyticalsolution (Table 4) assumes that the length of the electrodes is muchlarger than the electrode radius or separation distance between theelectrodes. Additionally, the analytical solution is not capable ofcapturing the non-linear electrical response of the tissue duringelectroporation procedures. The proposed statistical algorithm (Table 3)is preferably used in order to capture the response in treatments thatare being conducted clinically and show how the analytical overestimatesthe baseline and maximum current that uses the experimental data.

TABLE 3 Determination of conductivity using the statistical model and invivo data from pre-pulse and IRE pulses in canine kidney tissue usingidentical electrode configuration that the experimental one describedbelow. Current Voltage Volt-2-Dist Conductivity Z = [A] [V] [V/cm] [S/m]σ_(max)/σ_(min) Pre-Pulse 0.258 48 53 0.365 — IRE-Pulse 20.6 1758 19531.037 2.841 IRE-Pulse 23.7 1758 1953 1.212 3.320 IRE-Pulse 23.6 17581953 1.207 3.305 Avg. IRE 22.6 1758 1953 1.150 3.150 IRE-Pulse 10.4 12591399 0.727 1.990 IRE-Pulse 11.1 1257 1397 0.789 2.162 IRE-Pulse 11 12571397 0.781 2.138 Avg. IRE 10.8 1257 1397 0.763 2.090 Pre-Pulse 0.34373.3 52 0.341 — IRE-Pulse 23.6 2262 1616 1.007 2.952 IRE-Pulse 24.3 22621616 1.041 3.051 IRE-Pulse 25.4 2262 1616 1.094 3.207 Avg. IRE 24.5 22621616 1.050 3.080

TABLE 4 Determination of conductivity using the analytical model and invivo data from pre-pulse and IRE pulses in canine kidney tissue usingidentical electrode configuration than the experimental one describedbelow. Assumption: Length >> radius, Length >> width, 2 cylindricalelectrodes in an infinite medium. Current Voltage Volt-2-Dist ShapeConductivity [A] [V] [V/cm] Factor [m] [S/m] Pre-Pulse 0.258 48 530.01050 0.512 IRE-Pulse 20.6 1758 1953 0.01050 1.116 IRE-Pulse 23.7 17581953 0.01050 1.284 IRE-Pulse 23.6 1758 1953 0.01050 1.279 Avg. IRE 22.61758 1953 0.01050 1.225 IRE-Pulse 10.4 1259 1399 0.01050 0.787 IRE-Pulse11.1 1257 1397 0.01050 0.841 IRE-Pulse 11 1257 1397 0.01050 0.834 Avg.IRE 10.8 1257 1397 0.01050 0.819 Pre-Pulse 0.343 73.3 52 0.00924 0.506IRE-Pulse 23.6 2262 1616 0.00924 1.129 IRE-Pulse 24.3 2262 1616 0.009241.163 IRE-Pulse 25.4 2262 1616 0.00924 1.215 Avg. IRE 24.5 2262 16160.00924 1.172

Example 5 In Vivo Experiments

1) Animals.

IRE ablations were performed in canine kidneys in a procedure approvedby the local animal ethics committee. Male canines weighingapproximately 30 kg were premedicated with acetylpromazine (0.1 mg/kg),atropine (0.05 mg/kg), and morphine (0.2 mg/kg) prior to generalanesthesia induced with propofol (6 mg/kg, then 0.5 mg/kg/min) andmaintained with inhaled isofluorane (1-2%). Anesthetic depth wasmonitored by bispectral index monitoring (Covidien, Dublin, Ireland) ofEEG brain activity. After ensuring adequate anesthesia, a midlineincision was made and mesenchymal tissue was maneuvered to access thekidney. Pancuronium was delivered intravenously to mitigate electricallymediated muscle contraction, with an initial dose of 0.2 mg/kg, andadjusted if contractions increased.

2) Experimental Procedure.

Two modified 18 gauge needle electrodes (1.0 mm diameter and 1.0 cm inexposure) were inserted as pairs into the superior, middle, or inferiorlobe of the kidney, with lobes being randomly selected. A BTX ECM830pulse generator (Harvard Apparatus, Cambridge, Mass.) was used todeliver an initial 100 μs pre-pulse of 50 V/cm voltage-to-distance ratio(center-to-center) between the electrodes to get an initial current ableto be used to determine baseline conductivity. Electrical current wasmeasured with a Tektronix TCP305 electromagnetic induction current probeconnected to a TCPA300 amplifier (both Tektronix, Beaverton, Oreg.). AProtek DS0-2090 USB computer-interface oscilloscope provided currentmeasurements on a laptop using the included DSO-2090 software (both GSInstruments, Incheon, Korea). A schematic of the experimental setup canbe found in FIG. 14A. Following the pre-pulse, a series of 100 pulses,each 100 μs long, at a rate of 1 pulse per second was delivered,reversing polarity after 50 pulses. A five second pause was encounteredafter pulses 10 and 50 to save data. A schematic diagram showingdimension labeling conventions is shown in FIG. 14B. Representativecurrent waveforms from a pre-pulse and experimental pulse can be foundin FIGS. 14C and 14D, respectively. Electrode exposure lengths were setto 1 cm for all trials. The separation distance between electrodes andapplied voltage may be found in Table 5. After completing pulsedelivery, the electrodes were removed. Two additional ablations wereperformed in the remaining lobes before repeating the procedure on thecontralateral kidney, resulting in a total of three ablations per kidneyand six per canine.

TABLE 5 KIDNEY EXPERIMENT PROTOCOLS IN CANINE SUBJECTS Voltage-Separation, Distance Setup cm Voltage, V Ratio, V/cm n 1 1 1250 1250 4 21 1750 1750 4 3 1.5 2250 1500 6

3) Kidney Segmentation and 3D Reconstruction.

Numerical models provide an advantageous platform for predictingelectroporation treatment effects by simulating electric field,electrical conductivity, and temperature distributions. By understandingthe electric field distribution, one can apply an effective lethalelectric field threshold for IRE, E_(IRE), to predict ablation lesiondimensions under varying pulse protocols (electrode arrangements andapplied voltages). However, in order to do so, these models should firstbe calibrated with experimental data. Here, the numerical simulationalgorithm developed from porcine kidneys was expanded that accounts forconductivity changes using an asymmetrical sigmoid function (R. E. Neal,2nd, et al., “Experimental characterization and numerical modeling oftissue electrical conductivity during pulsed electric fields forirreversible electroporation treatment planning,” IEEE Trans BiomedEng., vol. 59, pp. 1076-85. Epub 2012 Jan. 6, 2012 (“R. E. Neal, 2^(nd),et al., 2012”)). The model is calibrated to the experimental lesions todetermine an effective electric field threshold under the threeexperimental setups used. In addition, static and linear conductivityfunctions are also correlated to the lesion dimensions. The threefunctions are used to evaluate which numerical technique will result inbetter accuracy in matching lesion shapes and resulting current fromactual IRE ablations in mammalian tissue, particularly for kidney.

The imaging-based computational model domains were constructed from amagnetic resonance imaging (MRI) scan of a kidney from a canine subjectof similar size to those in the study. The scans were scaled by 1.21times in all directions to better match the experimental kidneydimensions while maintaining the anatomical characteristics. Mimics 14.1image analysis software (Materialise, Leuven, BG) was used to segmentthe kidney geometry from the surrounding tissues. The kidney was tracedin each of the two-dimensional (2D) MRI axial slices, which were thenintegrated into a three-dimensional (3D) solid representation of thekidney volume which was refined and exported to 3-matic version 6.1(Materialise, Leuven, BG) to generate a volumetric mesh compatible withComsol Multiphysics finite element modeling software (ComsolMultiphysics, v.4.2a, Stockholm, Sweden).

Electrodes were simulated as paired cylinders, each 1 cm long and 1 mmin diameter, and separated by 1 or 1.5 cm to represent the twoexperimental conditions. The pairs were inserted into the 3D kidney meshin two configurations, representing both experimental approaches thatused either the superior/inferior (vertical) or middle (horizontal) lobeof the kidney, both with tips 1.5 cm deep. The finite element modelsimulated the electric field distribution in the kidney, which was usedto determine cell death EIRE by correlating the electric field valueswith the average in vivo lesion height and width dimensions.

4) Electric Field Distribution and Lethal E_(IRE) Determination.

The electric field distribution is determined according to−∇·(σ(|E|)∇ϕ)=0  (1)

where σ is the electrical conductivity of the tissue, E is the electricfield in V/cm, and ϕ is the electrical potential. Tissue-electrodeboundaries for the cathode and anode were defined as ϕ=V_(o) and ground,respectively. The remaining boundaries were treated as electricallyinsulating, dϕ/dn=0, since the kidneys were isolated from thesurrounding mesenchymal tissue during the experimental procedures. Thecurrent density was integrated over a mid-plane parallel to bothelectrodes to determine simulated electric current.

The model was solved for the vertical and horizontal electrodeconfigurations, each considering three electrical conductivity tissueresponses. These responses included a homogeneous static conductivity(σ₀) as well as two that accounted for electroporation basedconductivity changes in tissue that result from cell membranepermeabilization. The dynamic models are based on a relationship betweena minimum baseline and a maximum conductivity. The static conductivitymodel was used to determine the baseline conductivity, σ₀, by matchingsimulated electrical current with the pre-pulse experimental data, wherethe field strength should be below that able to permeabilize any cellsin the tissue. The maximum conductivity, σ_(max), occurs when the numberof cells electroporated in the tissue has saturated, and the cellularmembranes no longer restrict the extent of interstitial electrolytemobility. The statistical model discussed in (P. A. Garcia, et al.,“Towards a predictive model of electroporation-based therapies usingpre-pulse electrical measurements,” Conf Proc IEEE Eng Med Biol Soc,vol. 2012, pp. 2575-8, 2012 (“P. A. Garcia, et al., 2012”)) was used topredict σ_(max) from previously characterized tissue response topre-pulse σ₀ and electrical data.

The σ₀ and σ_(max) values provide the required parameters to define theelectric field-dependent conductivity, σ(|E|), of renal tissue in vivo.One model assumed a linear relationship that grew between the minimumand maximum conductivities over a range from 200 to 2000 V/cm,σ_(L)(|E|), and the second used an asymmetrical sigmoid Gompertz curve,σ_(S)(|E|), derived from the work described in (R. E. Neal, 2nd, et al.,2012) using the equation:σ_(S)(|E|)=σ₀+(σ_(max)−σ₀)·exp[−A·exp(−B·E)]  (2)

where A and B are unitless coefficients that vary with pulse length,t(s). This function was fit using curve parameters for a 100 μs longpulse, where A=3.053 and B =0.00233 (R. E. Neal, 2^(nd), et al., 2012)

The electric field distribution along a width and height projectionbased at the midpoint length of the electrodes was used to determine theelectric field magnitude that matched experimental lesion dimensions.This was performed for all three conductivity scenarios in all threeexperimental protocol setups in order to determine which model bestmatched the IRE ablations, providing the optimum conductivity modelingtechnique for mammalian tissue.

5) Results: In Vivo Experiments.

Electrical Currents.

All animals survived the procedures without adverse event untileuthanasia. Electrical pre-pulse currents were 0.258±0.036 A (mean±SD)for the 1 cm electrode separation trials and 0.343±0.050 A for the 1.5cm separation trials. Electrical currents from the trials for pulses1-10, 40-50, and 90-100 are reported in Table 6. Although currents aretypically reported to increase with consecutive pulses, there is nostatistically significant correlation between pulse number and measuredcurrent. Therefore, all numerical calibrations to match electricalcurrent and determine σ_(max) used the average current from all capturedpulses for each experimental setup.

TABLE 6 EXPERIMENTAL ELECTRIC CURRENTS TO CALIBRATE NUMERICAL MODELSSeparation, Average Pulse Average Electric Setup cm Delivered Voltage, VNumber Current, A* Pre 1 1 48 1750  0.258 (0.036) Pre 2 1.5 73 1250 0.343 (0.050) 1 1 1258 1-10 10.4 (1.7) 40-50  11.1 (1.1) 90-100 11.0(1.7) 2 2 1758 1-10 20.6 (3.2) 40-50  23.7 (5.1) 90-100 23.6 (3.8) 3 1.52262 1-10  23.6 (1.47) 40-50   24.3 (3.25) 90-100  25.4 (3.27) *Currentsgiven as “average (standard deviation)”

6) Determination of Dynamic Conductivity Function.

Pre-pulse electrical current was used to calculate the baselineconductivity, σ₀, used in the static numerical simulation. In addition,the baseline and maximum, σ_(max), electrical conductivities requiredfor generating the asymmetrical sigmoid and linear dynamic conductivityfunctions were calculated according to the procedure outlined in (P. A.Garcia, et al., 2012) and are provided in Table 7. The ratio betweenthese conductivities was calculated and demonstrates an increase inconductivity between 2.09 and 3.15 times, consistent with valuesdetermined in the literature for other organs (N. Pavselj, et al., “Thecourse of tissue permeabilization studied on a mathematical model of asubcutaneous tumor in small animals,” IEEE Trans Biomed Eng, vol. 52,pp. 1373-81, August 2005).

TABLE 7 BASELINE AND MAXIMUM ELECTRIC CONDUCTIVITIES Gap, V/d Ratio,Setup cm V/cm σ₀ σ_(max) σ_(max)/σ₀ 1 1 1250 0.365 0.763 2.09 2 1 17500.365 1.150 3.15 3 1.5 1500 0.341 1.050 3.08

Example 6 How to Use the Ratio of Maximum Conductivity to BaselineConductivity in Modifying the Electric Field Distribution and Thus theCassini Oval Equation

Irreversible electroporation (IRE) is a promising new method for thefocal ablation of undesirable tissue and tumors. The minimally invasiveprocedure involves placing electrodes into the region of interest anddelivering a series of low energy electric pulses to induceirrecoverable structural changes in cell membranes, thus achievingtissue death. To achieve IRE, the electric field in the region ofinterest needs to be above a critical threshold, which is dependent on avariety of conditions such as the physical properties of the tissue,electrode geometry and pulse parameters. Additionally, the electricconductivity of the tissue changes as a result of the pulses,redistributing the electric field and thus the treatment area. Theeffect of a dynamic conductivity around the electrodes where the highestelectric fields are generated was investigated in order to betterpredict the IRE treatment for clinical use.

The electric field distribution associated with the electric pulse isgiven by solving the governing Laplace equation, ∇·(σ∇φ)=0, where σ isthe tissue electrical conductivity (baseline 0.2 S/m) and φ theelectrical potential (3000 V). The dynamic changes in electricalconductivity due to electroporation were modeled with the flc2hsHeaviside function within the finite element modeling software used inthe study (Comsol Multiphysics 3.5a, Stockholm, Sweden). The dynamicconductivity factor ranged between 2.0-7.0 times the baseline value inthe regions exceeding 3000 V/cm. The total electrical current, volumes,and lesion shapes from the IRE treatment were evaluated.

FIGS. 15A and 15B display the electric field distributions for thenon-electroporated (baseline conductivity) and electroporated(maximum/baseline conductivity) maps, respectively. The electric fieldfrom using the baseline conductivity resulted in a “peanut” shapedistribution (FIG. 15A). By incorporating the conductivity ratio betweenσ_(max)/σ₀, there is a redistribution of the electric field and thus thevolumes, currents and lesion shapes are modified as well. The electricfield distribution for a 7.0× factor (FIG. 15B), shows a more gradualdissipation of the electric field and a rounder predicted IRE lesion.

A method to predict IRE lesions and incorporate the dynamic changes inconductivity due to electroporation around the electrodes is presentedin this example. This procedure provides additional tools to betterapproximate the electric field distributions in tissue and thus help togenerate more reliable IRE treatment planning for clinical use usingFinite Element Analysis (FEA) models.

Specifically in order to adapt the Cassini Oval to match experimentallesions or electric field distributions the following procedure shouldbe used:

In IRE treatments, the electric field distribution is the primary factorfor dictating defect formation and the resulting volume of treatedtissue (J. F. Edd and R. V. Davalos, “Mathematical modeling ofirreversible electroporation for treatment planning,” Technol Cancer ResTreat, vol. 6, pp. 275-286, 2007; D. Sel, et al., “Sequential finiteelement model of tissue electropermeabilization,” IEEE Trans Biomed Eng,vol. 52, pp. 816-27, May 2005; S. Mahnic-Kalamiza, et al., “Educationalapplication for visualization and analysis of electric field strength inmultiple electrode electroporation,” BMC Med Educ, vol. 12, p. 102, 2012(“S. Mahnic-Kalamiza, et al., 2012”)). The electric field is influencedby both the geometry and positioning of the electrodes as well as thedielectric tissue properties. Additionally, altered membranepermeability due to electroporation influences the tissue conductivityin a non-linear manner. Therefore numerical techniques are preferablyused to account for different electrode configurations and incorporatetissue-specific functions relating the electrical conductivity to theelectric field distribution (i.e. extent of electroporation). Theinventors are currently using imaging-based computational models for IREtreatment planning that use the physical properties of the tissue andpatient-specific 3D anatomical reconstructions to generate electricfield distributions (P. A. Garcia, et al., “Non-thermal irreversibleelectroporation (N-TIRE) and adjuvant fractionated radiotherapeuticmultimodal therapy for intracranial malignant glioma in a caninepatient,” Technol Cancer Res Treat, vol. 10, pp. 73-83, 2011 (“P. A.Garcia, et al, 2011”)).

Oftentimes in clinical practice, there is need to rapidly visualize theestimated zone of ablation without relying on complex and time consumingnumerical simulations. As an alternative, analytical solutions arepowerful techniques that provide valuable insight and offer the abilityto rapidly visualize electric field distributions (S. Mahnic-Kalamiza,et al., 2012). However, these analytical solutions assume infinitelylong electrodes which are not the case in clinical practice and do notincorporate the non-linear changes in tissue conductivity due toelectroporation. Therefore, there is a need for simple, quick, andaccurate methods to provide physicians with predicted IRE zones ofablation during surgery when one of the pulse parameters needs to beadjusted. To this end, the inventors have adapted the Cassini curve inan effort to provide researchers and physicians with a graphicalrepresentation of IRE zones of ablation, for example, in in vivo porcineliver. The goal of this work is to provide a correlation betweenexperimentally produced zones of ablations in in vivo porcine livertissue with the corresponding IRE pulse parameters and electrodeconfiguration. These Cassini curves are calibrated to experimental IREablations, and incorporate the dynamic changes in tissue conductivity, alimitation of the analytical approach.

The Cassini oval is a plane curve that derives its set of values basedon the distance of any given point, a, from the fixed location of twofoci, q₁ and q₂, located at (x₁, y₁) and (x₂, y₂). The equation issimilar to that of an ellipse, except that it is based on the product ofdistances from the foci, rather than the sum. This makes the equationfor such an oval└(x ₁ −a)²+(y ₁ −a)²┘·└(x ₂ −a)²+(y ₂ −a)² ┘=b ⁴  (3)

where b⁴ is a scaling factor to determine the value at any given point.For incorporation of this equation into shapes that mimic the electricfield distribution, it is assumed that the two foci were equidistantlylocated on the x-axis at (±x,0). The flexibility of the Cassini curve iscrucial since it allows for fitting a wide range of shapes by adjustingthe ‘a’ and/or ‘b’ parameters from Equation 3 simultaneously and fittingthem to the experimental lesion dimensions or the locations at which aparticular electric field value results from the computationalsimulations. The new approach in this analysis is that it is not assumedthat the parameter ‘a’ is related to the separation distance between theelectrodes used in IRE treatments for example but will be a secondparameter to match the width/depth of any distribution thus allowing formore flexibility between the shapes achieved with the Cassini Oval ascan be seen in FIGS. 16A and 16B.

The in vivo experimental data in porcine liver was provided frompublished studies performed at the Applied Radiology Laboratory ofHadassah Hebrew University Medical Center (P. A. Garcia, et al., 2011).All experiments were performed with Institutional Animal Care and UseCommittee approval from the Hebrew University Medical Center. Thetreatments were performed with a two-needle electrode configuration, 1.5cm center-to-center separation, 2.0 cm electrode exposure, and anapplied voltage of 2250 V. In this paper we only evaluate the effect ofpulse number and pulse duration on the resulting ‘a’ and ‘b’ parametersrequired to fit the IRE zones of ablation with the Cassini curve. TheNonlinearModelFit function in Wolfram Mathematica 9 was used todetermine the ‘a’ and ‘b’ parameters (average±standard deviation) foreach pulse parameter resulting in three curves for each condition. Thissame technique can be used to fit the ‘a’ and ‘b’ parameters to matchthe electric field shape at any particular electric field value as wellthus providing an avenue to capture the shape for any IRE lesionindependent of the tissue or patient.

The NonlinearModelFit results for the ‘a’ and ‘b’ parameters to generatethe Cassini curves are provided in FIG. 17. The ‘a’ parameter rangedfrom 0.75-1.04 and the ‘b’ from 1.06-1.35 for the average IRE zones ofablation in the in vivo porcine liver. From these data it can be seenthat each pulse parameter used results in a unique ‘a’ and ‘b’combination except for the twenty 100-μs pulses and ninety 20-μs pulseswhich overlap since they had identical IRE ablations. Therefore,consideration should be given to pulse length and total number of pulseswhen planning treatments to ensure maximum accuracy when using Cassinicurves to rapidly predict treatment zones.

FIG. 18 provides a representation of the average IRE zone of ablationand also includes the experimentally achieved standard deviations. ThisCassini curve is the most clinically relevant as ninety 100-μs pulses isthe recommended setting by the manufacturer that is currently being usedby physicians to treat several types of cancer. The Cassini curves inFIG. 18 were generated using two single needle electrodes witha=0.821±0.062 and b=1.256±0.079 that corresponded to IRE ablations thatwere 3.0±0.2 cm in width and 1.9±0.1 cm in depth (P. A. Garcia, et al.,2011). The results suggest that the Cassini curve is a viable method torepresent experimentally achieved IRE zones of ablation. These curvescan be used to provide physicians with simple, quick, and accurateprediction of IRE treatments. The parameters generated in this studywere achieved from porcine liver ablations data. The parameters forother tissues and/or tumors can be determined in a similar manner.Cassini curve parameters should be re-calibrated if the pulse parametersor electrode configuration (i.e. separation or exposure) deviate fromthe typical protocols in Ben-David et al. Additionally, there is a needto calibrate these Cassini curves to electric and temperaturedistributions in order to take advantage of the relatively simple curvesin representing simulated solutions that account for other pulseparameters and electrode configuration including different electrodeseparations, diameter, exposure, and voltages. A method to represent IREzones of ablation in a computationally efficient manner and based onexperimental data is thus presented. Such methods can be used to predictIRE ablation in liver in order to provide physicians with an immediatetool for treatment planning.

FIG. 19 is a representation of the 3D Electric Field [V/cm] Distributionin Non-Electroporated (Baseline) Tissue with 1.5-cm Single NeedleElectrodes at a Separation of 2.0 cm and 3000 V applied.

FIGS. 20A-D are representations of the Electric Field [V/cm]Distributions from the 3D Non-Electroporated (Baseline) Models with1.5-cm Electrodes at a Separation of 2.0 cm and 3000 V (cross-sections),wherein FIG. 20A is a representation of the x-y plane mid-electrodelength, FIG. 20B is a representation of the x-z plane mid-electrodediameter, FIG. 20C is a representation of the y-z plane mid electrodediameter, and FIG. 20D is a representation of the y-z plane betweenelectrodes.

FIG. 21 is a representation of the 3D Electric Field [V/cm] Distributionin Electroporated Tissue with 1.5-cm Single Needle Electrodes at aSeparation of 2.0 cm and 3000 V applied assuming σ_(max)/σ₀=3.6.

FIGS. 22A-22D are representations of the Electric Field [V/cm]Distributions from the 3D Electroporated Models with 1.5-cm Electrodesat a Separation of 2.0 cm and 3000 V (cross-sections) assuming aσ_(max)/σ₀=3.6, wherein FIG. 22A is a representation of the x-y planemid-electrode length, FIG. 22B is a representation of the x-z planemid-electrode diameter, FIG. 22C is a representation of the y-z planemid electrode diameter, and FIG. 22D is a representation of the y-zplane between electrodes.

Example 7 The Cassini Oval Equation

In mathematics, a Cassini oval is a set (or locus) of points in theplane such that each point p on the oval bears a special relation to twoother, fixed points q₁ and q₂: the product of the distance from p to q₁and the distance from p to q₂ is constant. That is, if the functiondist(x,y) is defined to be the distance from a point x to a point y,then all points p on a Cassini oval satisfy the equation:dist(q ₁ ,p)×dist(q ₂ ,p)=b ²  (2)where b is a constant.

Nevertheless, in embodiments the ‘b’ parameter can be modified tomanipulate the shape of the Cassini curve and illustrate the desiredelectric field distribution. Therefore, the ‘b’ is a variable parameterthat is determined based on the specific location (distance) of aparticular electric field threshold to be displayed.

The points q₁ and q₂ are called the foci of the oval.

Suppose q₁ is the point (a,0), and q₂ is the point (−a,0). Then thepoints on the curve satisfy the equation:((x−a)² +y ²)((x+a)² +y ²)=b ⁴  (3)

The equivalent polar equation is:r ⁴−2a ² r ² cos 2θ=b ⁴ −a ⁴  (4)

The shape of the oval depends on the ratio b/a. When b/a is greater than1, the locus is a single, connected loop. When b/a is less than 1, thelocus comprises two disconnected loops. When b/a is equal to 1, thelocus is a lemniscate of Bernoulli.

The Cassini equation provides a very efficient algorithm for plottingthe boundary line of the treatment zone that was created between twoprobes on grid 200. By taking pairs of probes for each firing sequence,the first probe is set as qi being the point (a,0) and the second probeis set as q₂ being the point (−a,0). This original Cassini ovalformulation was revised by modifying the assumption of the ‘a’ parameterbeing related to the position of the electrodes. In the revisedformulation the ‘a’ is a variable parameter that is adjusted dependingon the width and length of the Cassini oval in order to intercept thezone of ablation in the x- and y-directions.

In summary, the ‘a’ and ‘b’ variable parameters should be determined inorder to have the ability to generate a Cassini curve that could fit theshape of any electric field isocontour. Specifically from the electricfield simulations or experimental irreversible electroporation zones ofablation the user should determine the distance along the x-axis andy-axis that the Cassini curve should intersect.

For example in the case of a Finite Element Analysis (FEA) simulationusing two 1-mm in diameter electrodes, separated by a center-to-centerdistance of 2.0 cm, 1.5 cm in exposure, and an applied voltage of 3000 Vto one electrode and ground to the other electrode the distances fromthe point in between the electrodes to a specific electric field contouris given below (Table 8 for the baseline (non-electroporated) andσ_(max)/σ₀=3.6 (electroporated) models.

TABLE 8 E-field Baseline Baseline σ_(max)/σ₀ = 3.6 σ_(max)/σ₀ = 3.6[V/cm] (p_(1x), 0) [cm] (0, p_(2y)) [cm] (p_(3x), 0) [cm] (0, p_(4y))[cm] 300 1.97 0.92 2.38 1.39 400 1.81 0.69 2.17 1.18 500 1.70 0.49 1.991.01

Using the 500 V/cm electric field isocontour as an example it can bedetermined that the Cassini oval using the baseline model will intersectthe points (1.70,0) and (0,0.49) and the model using σ_(max)/σ₀=3.6 willintersect the point (1.99,0) and (0,1.01). Using the two points thatwill be intersected by the Cassini oval of each specific model type(non-electroporated vs. electroporated) allows for determination of the‘a’ and ‘b’ variable parameter and still satisfy the mathematicalcondition outlined above in the first paragraph of this section by wayof least square fits such as the NonlinearModelFit function inMathematica or via interpolation tables as the one presented below.

The interpolation method involves assuming values for the ‘a’ parameterfrom 0.00 cm to 3.00 cm in steps of 0.01 cm and calculating the ‘b’parameter using the specific points from the previous paragraph. Thedistance and steps were arbitrarily chosen and can vary depending on thespecific Cassini oval that is being developed. In the case of Table 9the point p1x=(1.70 cm, 0 cm) and the point p2y=(0 cm, 0.49 cm) and thecorresponding distances to either q1 (−a,0) or q2 (a,0) are calculated.

TABLE 9 d(q1, d(q2, d(q1, d(q2, p1x) = p1x) = p2y) = p2y) = d1*d2/ ‘a’d1 d2 d1*d2 d3 d4 d3*d4 d3*d4 1.04 0.66 2.74 1.808 1.150 1.150 1.3221.37 1.05 0.65 2.75 1.788 1.159 1.159 1.343 1.33 1.06 0.64 2.76 1.7661.168 1.168 1.364 1.30 1.07 0.63 2.77 1.745 1.177 1.177 1.385 1.26 1.080.62 2.78 1.724 1.186 1.186 1.407 1.23 1.09 0.61 2.79 1.702 1.195 1.1951.428 1.19 1.1 0.60 2.80 1.680 1.204 1.204 1.450 1.16 1.11 0.59 2.811.658 1.213 1.213 1.472 1.13 1.12 0.58 2.82 1.636 1.222 1.222 1.495 1.091.13 0.57 2.83 1.613 1.232 1.232 1.517 1.06 1.14 0.56 2.84 1.590 1.2411.241 1.540 1.03 1.15 0.55 2.85 1.568 1.250 1.250 1.563 1.00 1.16 0.542.86 1.544 1.259 1.259 1.586 0.97 1.17 0.53 2.87 1.521 1.268 1.268 1.6090.95 1.18 0.52 2.88 1.498 1.278 1.278 1.633 0.92 1.19 0.51 2.89 1.4741.287 1.287 1.656 0.89 1.2 0.50 2.90 1.450 1.296 1.296 1.680 0.86 1.210.49 2.91 1.426 1.305 1.305 1.704 0.84 1.22 0.48 2.92 1.402 1.315 1.3151.729 0.81 1.23 0.47 2.93 1.377 1.324 1.324 1.753 0.79 1.24 0.46 2.941.352 1.333 1.333 1.778 0.76

In the baseline case analyzed above when the variable parameter ‘a’ was1.15 cm the calculated b² were 1.568 and 1.563 for the d1*d2 and d3*d4,respectively. The last column calculates the ratio of both b² values inorder to determine the location at which they are the same (or closest)which happens when (d1*d2)/(d3*d4)=1.00.

Once it is determined that ‘a’=1.15 cm provides the closest ratio toone, the average of the d1*d2 (1.568) and d3*d4 (1.563) quantities iscalculated and used to determine the corresponding ‘b’ parameter bytaking the square root as shown in the equation below.

$\begin{matrix}{b = {\sqrt{\frac{\left( {d\; 1*d\; 2} \right) + \left( {d\; 3*d\; 4} \right)}{2}} = {\sqrt{\frac{1.568 + 1.563}{2}} = {\sqrt{1.5655} = 1.2512}}}} & (5)\end{matrix}$

Once the ‘a’ and ‘b’ parameters are determined then any plottingsoftware can be used to illustrate the Cassini curve in Cartesiancoordinates using the modified equationy=±√{square root over (−a ² −x ²±√{square root over (b ⁴+4a ² x²)})}  (6)

The steps outlined in the previous paragraphs just above can also beused to determine the ‘a’ and ‘b’ parameters using the same methodologyand with points p3x=(1.99 cm, 0 cm) and p4y=(0 cm, 1.01 cm) and resultsin ‘a’=1.21 cm and ‘b’=1.578 cm as the Cassini parameters for theelectroporated model when σ_(max)/σ₀=3.6.

TABLE 10 d(q1, d(q2, d(q1, d(q2, p3x) = p3x) = p4y) = p4y) = d5*d6/ ‘a’d5 d6 d5*d6 d7 d8 d7*d8 d7*d8 1.1 0.89 3.09 2.750 1.493 1.493 2.230 1.231.11 0.88 3.10 2.728 1.501 1.501 2.252 1.21 1.12 0.87 3.11 2.706 1.5081.508 2.275 1.19 1.13 0.86 3.12 2.683 1.516 1.516 2.297 1.17 1.14 0.853.13 2.661 1.523 1.523 2.320 1.15 1.15 0.84 3.14 2.638 1.531 1.531 2.3431.13 1.16 0.83 3.15 2.615 1.538 1.538 2.366 1.11 1.17 0.82 3.16 2.5911.546 1.546 2.389 1.08 1.18 0.81 3.17 2.568 1.553 1.553 2.413 1.06 1.190.80 3.18 2.544 1.561 1.561 2.436 1.04 1.2 0.79 3.19 2.520 1.568 1.5682.460 1.02 1.21 0.78 3.20 2.496 1.576 1.576 2.484 1.00 1.22 0.77 3.212.472 1.584 1.584 2.509 0.99 1.23 0.76 3.22 2.447 1.592 1.592 2.533 0.971.24 0.75 3.23 2.423 1.599 1.599 2.558 0.95 1.25 0.74 3.24 2.398 1.6071.607 2.583 0.93 1.26 0.73 3.25 2.373 1.615 1.615 2.608 0.91 1.27 0.723.26 2.347 1.623 1.623 2.633 0.89 1.28 0.71 3.27 2.322 1.630 1.630 2.6590.87 1.29 0.70 3.28 2.296 1.638 1.638 2.684 0.86 1.3 0.69 3.29 2.2701.646 1.646 2.710 0.84

In FIG. 23, it can be seen that with the implementation of the pre-pulseconcept to determine the ratio of maximum conductivity to baselineconductivity one can derive a Cassini curve representing zones ofablation. In this case the 500 V/cm isocontour was specified but thistechnique could be used for any other isocontour that perhaps couldrepresent the lethal IRE threshold for any other tissue/tumor type.

The polar equation for the Cassini curve could also be used becausesince it provides an alternate method for computation. The currentCartesian coordinate algorithm can work equally as well by using thepolar equation of the Cassini curve. By solving for r² from eq. (4)above, the following polar equation was developed:r ² =a ² cos(2*theta)+/−sqrt(b ⁴ −a ⁴ sin²(2*theta))  (5)

and the ‘a’ and ‘b’ parameters should be determined as previouslydescribed in this application.

Example 8 Mapping of Electric Field and Thermal Contours Using aSimplified Data Cross-Referencing Approach

This method can be used to identify the volume of tissue which will beelevated above a specific temperature (e.g. 45° C.) for specifictreatment parameters. This contour can then be correlated with electricfield intensity. This data in turn can be used to fit a contour usingthe Cassini oval software in the NANOKNIFE® System.

Methods: A mathematical model was built with COMSOL Multiphysics(Version 4.2a, Comsol Inc., Burlington, Mass., USA) to estimate thetemperature rise within tissue due to Joule heating effects. Theelectric field distribution within the simulation domain was solvedusing the Joule Heating module, as described by the Laplace Equation:∇²ϕ=0

where ϕ is the electric potential, this equation is solved with boundaryconditions:

{right arrow over (n)}·{right arrow over (J)}=0 at the boundaries

ϕ=V_(in) at the boundary of the first electrode

ϕ=0 at the boundary of the second electrode

wherein {right arrow over (n)} is the normal vector to the surface,{right arrow over (J)} is the electrical current and V_(in) is theelectrical potential applied. Heat transfer in the solid domain wascalculated as:

${\rho\; C_{p}\frac{\partial T}{\partial t}} = {{\nabla{\cdot \left( {k{\nabla T}} \right)}} + {Q_{jh}\left\lbrack \frac{W}{m^{3}} \right\rbrack}}$

where ρ is the density, C_(p) is the heat capacity, k is the thermalconductivity, and Q_(jh) are the resistive losses

$Q_{jh} = {J \cdot {E\left\lbrack \frac{W}{m^{3}} \right\rbrack}}$

where J is the induced current density

$J = {\sigma\;{E\left\lbrack \frac{A}{m^{2}} \right\rbrack}}$

and σ is the tissue conductivity and E is the electric field

$E = {- {\nabla{\phi\left\lbrack \frac{V}{m} \right\rbrack}}}$

To account for the pulsed nature of the applied electric field, theJoule heating term in COMSOL was adjusted by adding in a duty cycle termequal to 100×10⁻⁶, the pulse duration (100 μs) (See P. A. Garcia, etal., “A Parametric Study Delineating Irreversible Electroporation fromThermal Damage Based on a Minimally Invasive Intracranial Procedure,”Biomed Eng Online, vol. 10, p. 34, Apr. 30, 2011).

In the Joule Heating Model equation view, the equation for resistivelosses was modified to:jh·Qrh=((jh·Jix+jh·Jex)*duty_cycle*jh·Ex(jh·Jiy+jh·Jey)*duty_cycle*jh·Ey+(jh·Jiz+jh·Jez)*duty_cycle*jh·Ez)*(t<=90)+0*(t>90)

The resulting behavior was to calculate Joule heating only for the first90 seconds (Ninety pulses of 100 μs each) of the simulation, afterwhich, heat was allowed to dissipate within the tissue domain withoutadditional heating. The parameters used in the simulations are providedin Table 11 below.

TABLE 11 Parameters used in COMSOL finite element model Parameter ValueUnit Description r_e 0.0005 [m] electrode radius l_e 0.15 [m] electrodelength l_t 0.15 [m] tissue radius h_t 0.1 [m] tissue thickness gap 0.015[m] center-to-center spacing epsi_e 0 — electrode permittivity epsi_i 0— insulation permittivity epsi_t 0 — tissue permittivity sigma_e2.22E+06 [S/m] electrode conductivity sigma_i 6.66E−16 [S/m] insulationconductivity sigma_t 0.2 [S/m] tissue conductivity rho 1080 [kg/m3]tissue density Cp 3890 [J/(kg * K)] tissue heat capacity k 0.547 [W(m *K)] tissue thermal conductivity duty_cycle 1.00E−04 — pulse duty cycle

Results: The COMSOL model was used to solve for temperaturedistributions at times between 0 and 900 seconds (10 second increment0-100s, 100 second increment 100-900 seconds). Electric Field andTemperature distributions were exported along lines on the x-(width) andy-axis (depth) with 100 micrometer spacing between data points. Thesevalues were imported into Excel and used as the basis for the Cassinioval calculations. FIGS. 24A-D shows the temperature distributionsdetermined in COMSOL at 90 seconds (Ninety pulses of 100 μs each) for3000 V treatments with 1.0 cm, 1.5 cm, 2.0 cm, and 2.5 cm electrodespacing and an electrode exposure of 1.5 cm. Contours on this figureshow an approximate electric field which corresponds to tissuetemperatures greater than 45° C. Simulations of each parameter requiredapproximately 30 minutes to complete for a total computational durationof 15 hours.

FIGS. 25A-D shows the Cassini oval approximations for the temperatureand electric field distributions based on the finite element simulationresults. Iso-contour lines correspond to the tissue with temperatureelevated above 45° C. and electric field above 500 V/cm, at the end of a90 second IRE treatment (Ninety pulses of 100 μs).

The Cassini oval spreadsheet has been programmed so that the user canplot contour lines for specified voltages (500, 1000, 1500, 2000, 2500,3000 V), electrode separations (0.5, 1.0, 1.5, 2.0, 2.5 cm), Simulationtimes (0-900 seconds), Temperatures (37-Tmax ° C.), and electric fieldintensities (0-infinity V/cm). FIGS. 26A-D shows the temperaturedistributions for a 3000 V, 2.5 cm spacing treatment at 10, 40, 90, and200 seconds. The simulation accounts for Joule heating up to 90 seconds.After 90 seconds, Joule heating is no longer calculated and thetemperature dissipates over time since the ninety-pulse delivery iscompleted.

The Cassini oval approximation can also be used to investigate thecontours of any temperature. FIG. 27A-D shows the volumes of tissue thathave been heated by at least 0.2, 3.0, 8.0, and 13.0° C. At 3000V, 1.5cm exposure, and 2.5 cm electrode spacing at a time=90 seconds (Ninetypulses of 100 μs each), only a very small volume of tissue outside theablation zone (500 V/cm) experiences any temperature increase.

The Cassini oval approximation tool provides a rapid method fordetermining the temperature distribution expected for a given set oftreatment parameters (FIGS. 28 and 29). Voltage, Electrode Spacing(Gap), Time, Temperature, and Electric Field can be selected by movingthe slider or editing values in the green boxes. In embodiments,baseline conductivity of the target treatment area, and/or aconductivity for a specific tissue type, and/or a change in conductivityfor the target treatment area can also, and/or alternatively, beselected. Voltage is selectable in 500 V discrete steps between 500 and3000 V. Electrode Spacing (Gap) is selectable in 5.0 mm discrete stepsbetween 5.0 mm and 25 mm. Time is selectable in 10 second discrete stepsbetween 0 and 100 seconds and 100 second discrete steps between 100 and900 seconds. The temperature contour line is selectable for any valuebetween 37° C. and T_(max), where T_(max) is the maximum temperature inthe tissue at a given treatment time. Additionally, the electric fielddistribution within the tissue can be set for any value.

Additional examples of usage of the Cassini oval approximation tool areshown in the following figures. FIGS. 30A-D show temperature contourlines for 40° C. (FIG. 30A), 45° C. (FIG. 30B), 50° C. (FIG. 30C), and55° C. (FIG. 30D) for a 90 second IRE treatment (Ninety pulses of 100 μseach) with a voltage of 3000 V and electrode spacing of 10 mm. Anelectric field contour line of 500 V/cm is shown for comparison. As canbe seen, the figures show a temperature gradient that expectedlyincreases from the 500 V/cm contour line toward the electrodes.

FIGS. 31A-D show contour lines representing a 40° C. temperature and a500 V/cm electric field for a 90 second IRE treatment (Ninety pulses of100 μs each) and electrode spacing of 10 mm at different voltages (3000V(FIG. 31A), 2000V (FIG. 31B), 1500V (FIG. 31C), and 1000V (FIG. 31D)).The figures show that the size of the electric field and heated areadecreases in proportion to the decrease in voltage.

FIGS. 32A-D show electric field contour lines for 500 V/cm (FIG. 32A),1000 V/cm (FIG. 32B), 1500 V/cm (FIG. 32C), and 2000 V/cm (FIG. 32D) fora 90 second IRE treatment (Ninety pulses of 100 μs each) with a voltageof 3000 V and electrode spacing of 10 mm. As can be seen, the figuresshow an electric field gradient that expectedly increases from the 40°C. contour line toward the electrodes.

FIGS. 33A-D show contour lines representing a 40° C. temperature and a500 V/cm electric field for a 90 second IRE treatment (Ninety pulses of100 μs each) and voltage of 3000V at different electrode spacings (5 mm(FIG. 33A), 10 mm (FIG. 33B), 15 mm (FIG. 33C), 20 mm FIG. 33D)). As canbe seen, increasing the electrode distance up to 15 mm widens theelectric field and temperature contour. At an electrode distance of 20mm, the electric field contour line widens and narrows, but the areaheated to at least 40° C. is limited to a radius around each electrode.

FIGS. 34A-D show contour lines representing a 40° C. temperature and a500 V/cm electric field for an IRE treatment of 3000V and an electrodespacing of 10 mm at different durations of treatment (90 seconds (Ninetypulses of 100 μs each) (FIG. 34A), 60 seconds (Sixty pulses of 100 μseach) (FIG. 34B), 30 seconds (Thirty pulses of 100 μs each) (FIG. 34C),10 seconds (Ten pulses of 100 μs each) (FIG. 34D)). The graphs show thatdecreasing the durations of treatment reduces the area heated at least40° C., but not the area of the electric field.

Model Limitations: This model was designed to give a rapid approximationfor the temperature distribution within a volume of tissue without theneed for complex finite element simulations. The data used to fit theCassini oval curves uses values calculated assuming a constantconductivity of 0.2 S/m. This represents an approximate conductivity ofhuman tissue, though conductivities of tissue vary between patients,tissue types, locations, and pathologies. Changing conductivity due totemperature increases or electroporation effects were not included. FIG.35 shows the COMSOL three-dimensional finite element domain mesh used tocalculate the electric field and temperature information to create theCassini Oval values and curves.

The effects of blood flow and perfusion through the tissue, metabolicheat generation, or diffusion of heat at the tissue domain boundarieswere not considered. It is anticipated that these effects will result inlower temperatures. Therefore, the visualization tool provides aconservative (worst case scenario) estimate as to the zones exposed tocritical temperatures. The effects of changing conductivity andconductivities other than 0.2 S/m were not considered. Elevatedconductivities are anticipated to result in higher temperatures withinthe tissue. Blood flow, metabolic heat generation, tissue conductivity,and ratios of changing conductivity are tissue type specific and willrequire the inclusion of in-vivo derived data.

Conclusions: In this Example, a real time visualization package plotsthe isocontour lines for an arbitrary temperature and electric fieldbased on applied voltage, electrode spacing, and time. This data can beused to build intuition and instruct clinicians on reasonableexpectations of temperature increases to prevent damage to criticalstructures of organs in the proximity of the treatment.

Example 9 Visualization of Electric Field Distributions Using DifferentConfigurations of Bipolar Probes

FIGS. 36A-36C show a representation of a visualization tool providingthe 650 V/cm electric field distributions using different configurationsof bipolar probes and includes dynamic change (3.6×) in electricalconductivity from the non-electroporated baseline for runs 7, 8, and 9of the visualization. FIG. 36D is a table showing parameters of each runincluding electrode length, separation distance (insulation), andapplied voltage. FIG. 36E is a table showing lesion dimensions for runs7, 8, and 9. The results show that as the length of the bipolarelectrode increases, the size of the zone of ablation increases.

Example 10 Determining the IRE Threshold for Different Tissues Accordingto Conductivity

In this Example, as shown in the following figures, the “Goldberg” data(red-dashed line), is from pre-clinical data for a particular treatment(2700V, 90 pulses, 100 μs energized per pulse). By adjusting one or moretreatment parameters, a user can determine the electric field thresholdfor these types of tissues (black-solid line).

An important aspect of this model is that the tissue conductivity isallowed to change as a function of electric field to simulate whathappens when the tissue becomes irreversibly electroporated. Thisfunction is ‘sigmoidal’ or ‘S’ shaped and increases from a baseline(non-electroporated) to a conductivity multiplier (electroporated). Thistransition happens at a specific electric field intensity.

In FIG. 37, the conductivity changes from 0.1 to 0.35 at an electricfield centered at 500 V/cm. A user can change/shift all of the values inthis curve to fit the experimental data. FIG. 38A is a contour plotcomparing the “Goldberg” data (red dashed line) with a calculatedthreshold (solid black line) based on the parameters shown in FIG. 38C,explained below. FIG. 38B is a contour plot comparing the conductivity(blue dotted line) with a calculated threshold (solid black line) basedon the parameters shown in FIG. 38C.

IRE Threshold [V/cm]: This parameter is the electric field at which thechange in conductivity occurs for the sigmoidal curve. By changing thisvalue, the sigmoidal curve shifts to the left or right. A value of 500V/cm has been found to fit the data best.

Transition zone: This is the ‘width’ of the transition zone. By changingthis value, the rate at which the conductivity increase changes. In FIG.37, this value is set to 0.49, the widest transition possible. It hasbeen found that a transition of 0.2 matches the experimental data best.

Sigma: This is the baseline conductivity before treatment. It has beenfound that a value of 0.067 (or 0.1) works well.

Conductivity Multiplier: This is how much the conductivity increases bywhen the tissue has been irreversibly electroporated. A 3.6× increasehas been found experimentally for liver and fits the data well.

E-Field: This is the parameter that is adjusted to find the in-vivoirreversible electroporation threshold. With the values set for theother parameters above, it has been found that IRE should occur at athreshold of 580 V/cm to match the lesions found in-vivo.

The following figures show how modifying the conductivity of the tissuechanges the calculated zone of ablation. FIGS. 39A-39F were performedaccording to the parameters in FIG. 38C, except the conductivity of thetissue was modified. FIGS. 39A-39C show the “Goldberg” data andcalculated threshold and FIGS. 39D-39F show the conductivity andcalculated threshold for conductivity multipliers of 2, 3, and 4,respectively. As can be seen, the calculated ablation zone increases incomparison to the Goldberg preclinical data as conductivity increases.

FIGS. 40A-40F were performed for an IRE Threshold of 600 V/cm, atransition zone of 0.4, a Voltage of 700 V, an E-Field of 700 V/cm, anda Sigma (electrical conductivity) of 0.20 S/m. FIGS. 40A-40C show the“Goldberg” data and calculated threshold and FIGS. 40D-40F show theconductivity and calculated threshold for conductivity multipliers of 2,3, and 4, respectively.

FIGS. 41A-41F were performed for an IRE Threshold of 1000 V/cm, atransition zone of 0.2, a Voltage of 2700 V, an E-Field of 700 V/cm, anda Sigma (electrical conductivity) of 0.20 S/m. FIGS. 41A-41C show the“Goldberg” data and calculated threshold and FIGS. 41D-41F show theconductivity and calculated threshold for conductivity multipliers of 2,3, and 4, respectively.

As can be seen, the calculated ablation zone increases in comparison tothe Goldberg preclinical data as the conductivity multiplier increases.

Example 11 Correlating Experimental and Numerical IRE Lesions Using theBipolar Probe

Purpose: To establish a function that correlates experimentally producedzones of ablations in in vivo porcine tissue with the corresponding IREpulse parameters (duration, number, strength) and single needleelectrode configuration.

A mathematical function was developed that captures the IRE response inliver tissue as a function of applied voltage, pulse number, and pulseduration for the bipolar electrode configuration. It is important tonote that the inventors used a rate equation that was fit to the 1.5cm×2.9 cm IRE zone of ablation but this has not been validatedexperimentally (See Golberg, A. and B. Rubinsky, A statistical model formultidimensional irreversible electroporation cell death in tissue.Biomed Eng Online, 2010. 9(1): p. 13). The results below provide insightas to the effect of different pulse parameters and electrode/insulationdimensions in the resulting zone of IRE ablation in order to optimizethe bipolar probe electrode for clinical use. In order to perform acomputationally efficient study, the models were constructed in a 2-Daxis-symmetric platform which generates results that are representativeof the 3-D space.

Part 1: The work from Part 1 determined the electric field threshold for0.7 cm electrodes with a 0.8 cm insulation to be 572.8 V/cm assuming astatic electric conductivity (Table 12). This threshold is the averagebetween the width (349.5 V/cm) and length (795.1V/cm) electric fieldthresholds that matched the experimental lesion of 1.5 cm (width) by 2.9cm (length). It is important to note that due to the mismatch betweenthe electric field thresholds, the predicted width will beunderestimated and the predicted length will be overestimated when usingthe average value of 572.8 V/cm. The model assumes an applied voltage of2700 V, ninety 100-μs pulses, at a repetition rate of 1 pulse persecond, and a viability value of 0.1% (S=0.001) as the complete celldeath due to IRE exposure (FIG. 42). The rate equation used in theanalysis is given by S=e^(−k·E·t) where S is the cell viabilitypost-IRE, E is the electric field, t is the cumulative exposure time,and k is the rate constant that dictates cell death. Specifically duringthis Part, it was determined that k=1.33996 assuming an E=572.8 V/cm,S=0.001, and t=0.009 s (90×100-μs). The k parameter was scaled by theduty cycle of the pulses (0.0001 s) in order to reflect the cellviability in the time scale in which the pulses were delivered (i.e. onepulse per second).

TABLE 12 Electric field thresholds for the static modeling approach fromexperimental IRE lesions in liver. Lesion E-field Average ThresholdConductivity Dimensions [V/cm] [V/cm] [V/cm] Static-σ₀ x = 1.5 cm 349.5349.5 572.8 Static-σ₀ y = 2.9 cm (distal) 796.2 795.1 Static-σ₀ y = 2.9cm 795.6 (proximal)

A parametric study was constructed in order to explore the effect ofelectrode diameter (18G=1.27 mm, 16G=1.65 mm, 14G=2.11 mm), electrodespacing (0.4 cm, 0.8 cm, 1.2 cm, 1.6 cm), and electrode length (0.5 cm,0.75 cm, 1.0 cm, 1.25 cm, and 1.5 cm). In order to provide acomprehensive analysis of all iterations we computed the volumes oftissue that would achieve a cell viability, S<0.001, and these resultsare reported in the table of FIG. 48A-B. The results with the specificminimum and maximum parameters from Part 1 are presented in Table 13 anddemonstrate that with increasing probe diameter and electrode length alarger area/volume of IRE ablation is achieved for ninety 100-μs pulsesdelivered at 2700 V at a repetition rate of one pulse per second. FIGS.43A-D shows the predicted regions of post-IRE cell viability isocontourlevels with the solid white curve illustrating the 0.1%, 1.0%, and 10%cell viability levels. Of importance is the fact that if the electrodesare spaced too far apart, the resulting IRE zone of ablation is notcontiguous and the treatment would fail between the electrodes as shownwith Runs 60 and 10, respectively.

TABLE 13 Predicted IRE lesion dimensions for the min. and max.parameters investigated in Part 1. Spac- Vol- Diam- ing Length Area umeRun eter (cm) (cm) (cm²) (cm³) x(cm) y(cm) x:y 60 14 G = 1.6 1.5 2.7056.232 0.311 5.550 0.056 2.11 mm 10 18 G = 1.6 0.5 1.042 1.689 0.2273.390 0.067 1.27 mm 49 18 G = 0.4 1.5 2.242 4.626 1.257 4.210 0.299 1.27mm 3 14 G = 0.4 0.5 1.120 2.241 1.221 2.190 0.558 2.11 mm

In an effort to better understand the effects of the electrode geometryon the ablation region an extra set of values (Table 14) was generated.The closest outputs to a 1.5 cm×2.9 cm lesion size from parameters inTable 13 were modified to better approximate the targeted lesion.Considering all 60 different runs, number 15 is closest to the targetedvalues with a lesion geometry of 1.301 cm×2.84 cm.

TABLE 14 Predicted IRE lesion dimensions for parameters approximating a1.5 cm × 2.9 cm ablation region. Spac- Vol- Diam- ing Length Area umeRun eter (cm) (cm) (cm²) (cm³) x(cm) y(cm) x:y 3 14 G = 0.4 0.5 1.1202.241 1.221 2.190 0.558 2.11 mm 1 18 G = 0.4 0.5 0.943 1.590 1.037 2.1700.478 1.27 mm 15 14 G = 0.4 0.75 1.483 3.215 1.301 2.840 0.458 2.11 mm18 14 G = 0.8 0.75 1.680 3.652 1.181 3.250 0.363 2.11 mm

Part 2: In Part 2 the electric field distribution assuming a dynamicelectric conductivity was used to determine the threshold of cell deathdue to IRE exposure. Specifically during this Part, a sigmoid function(FIG. 44) with a baseline (0.067 S/m) and maximum (0.241 S/m)conductivity values was used (see Sel, D., et al., Sequential finiteelement model of tissue electropermeabilization. IEEE Trans Biomed Eng,2005. 52(5): p. 816-27). This published function assumes that reversibleelectroporation starts at 460 V/cm and is irreversible at 700 V/cm asreported by Sel. et al. Using the dynamic conductivity function resultedin a more consistent electric field threshold between the width (615.7V/cm) and the length (727.4 V/cm); therefore, using the average(670.1V/cm) provides a better prediction of the IRE lesions beingachieved in vivo versus the ones predicted in Part 1 that assume astatic conductivity (Table 15). The electric field threshold for IREusing the dynamic conductivity approach resulted in a revised k=1.14539assuming an E=670.1V/cm, S=0.001, and t=0.009 s (90×100 μs). The kparameter was scaled by the duty cycle of the pulses (0.0001s) in orderto reflect the cell viability in the time scale in which the pulses weredelivered (i.e. one pulse per second).

TABLE 15 Electric field thresholds for the dynamic modeling approachfrom experimental IRE lesions in liver. E-field Threshold ConductivityIRE Dimension [V/cm] Average [V/cm] Dynamic- x = 1.5 cm 615.7 615.7670.1 σ(E) Dynamic- y = 2.9 cm (distal) 720.7 727.4 σ(E) Dynamic- y =2.9 cm 734.0 σ(E) (proximal)

In Part 2, the effect of pulse strength (2000 V, 2250 V, 2500 V, 2750 V,3000 V) and pulse number (20, 40, 60, 80, 100) was explicitlyinvestigated and the results of the parametric study are provided in thetable of FIG. 49 and a representative plot provided in FIG. 45. Theresults with the specific minimum and maximum parameters from Part 2 arepresented in

Table 16 and demonstrate that with increasing pulse strength and pulsenumber a larger volume of IRE ablation is achieved at a repetition rateof one pulse per second (FIGS. 46A-D). In order to compare the resultsto the electric field threshold, both areas/volumes were computed andare provided as well. Similar to the results from Part 1, the whitesolid curve represents the 0.1%, 1.0%, and 10% cell viability isocontourlevels due to IRE. For all voltages investigated, delivering one hundred100-μs pulses covers a greater area/volume than the prediction by the670.1 V/cm electric field threshold assumed with the dynamicconductivity function.

TABLE 16 Predicted lesion dimensions for the minimum and maximumparameters investigated in Part 2. Volt- Vol- E- E- age Num- Area umeField Field Run (V) ber (cm²) (cm³) (cm²) (cm³) x(cm) y(cm) x:y 3 200020 0.080 0.050 0.970 1.575 0.216 2.350 0.092 6 2000 100 1.209 2.2380.970 1.575 0.646 1.630 0.396 27 3000 20 0.209 0.170 1.493 3.171 0.2211.800 0.123 30 3000 100 1.900 4.604 1.493 3.171 0.946 1.130 0.837

Part 3: In this Part the exposure of liver tissue to 300 (5×60) and 360(4×90) pulses were simulated at an applied voltage of 3000 V, 100-μspulses, at a repetition rate of one pulse per second. From the cellviability plots in FIG. 47A-B it can be seen that with increasing numberof pulses, larger zones of IRE ablation are achieved with thecorresponding areas and volumes included in Table 17 and the table ofFIG. 50. It is important to note that in this case the simulationassumes that there is sufficient thermal relaxation time between sets ofpulses; thus preventing any potential thermal damage from Joule heatingwhich is not simulated in this work.

TABLE 17 Predicted lesion dimensions for the 5 × 60 and 4 × 90 IREpulses investigated in Part 3. Vol- Vol- E- E- tage Num- Area ume FieldField Run (V) ber (cm²) (cm³) (cm²) (cm³) x(cm) y(cm) x:y 16 3000 5 ×6.135 27.282 1.493 3.171 2.877 4.900 0.587 60 19 3000 4 × 6.950 33.2021.493 3.171 3.287 5.540 0.593 90

Models with exploratory geometries were developed that include multiplevoltage sources and current diffusers (balloons). FIGS. 51A-C presentimages of the raw geometries being tested and FIGS. 51D-F show thecorresponding electric field distribution. In general, the mostinfluential parameter remains the size of the electrodes and insulation.According to the values generated from these simulations, it seems likesubstantial helps to achieve more spherical lesions.

TABLE 18 Predicted IRE lesion dimensions for exploratory models inAppendix D. Spac- Vol- Diam- ing Length Area ume Run eter (cm) (cm)(cm²) (cm³) x(cm) y(cm) x:y 61 0.211 0.4 0.5 1.453 1.807 1.201 2.8500.421 62 0.211 0.4 1 1.617 2.129 1.321 3.670 0.360 63 0.211 0.4 1 2.0083.041 1.241 2.955 0.420 64 0.211 0.4 0.5 1.389 1.929 1.261 2.810 0.44965 0.211 0.4 0.5 0.976 1.142 1.421 2.000 0.711

The present invention has been described with reference to particularembodiments having various features. In light of the disclosureprovided, it will be apparent to those skilled in the art that variousmodifications and variations can be made in the practice of the presentinvention without departing from the scope or spirit of the invention.One skilled in the art will recognize that the disclosed features may beused singularly, in any combination, or omitted based on therequirements and specifications of a given application or design. Otherembodiments of the invention will be apparent to those skilled in theart from consideration of the specification and practice of theinvention.

It is noted in particular that where a range of values is provided inthis specification, each value between the upper and lower limits ofthat range is also specifically disclosed. The upper and lower limits ofthese smaller ranges may independently be included or excluded in therange as well. The singular forms “a,” “an,” and “the” include pluralreferents unless the context clearly dictates otherwise. It is intendedthat the specification and examples be considered as exemplary in natureand that variations that do not depart from the essence of the inventionfall within the scope of the invention. In particular, for methodembodiments, the order of steps is merely exemplary and variationsappreciated by a skilled artisan are included in the scope of theinvention. Further, all of the references cited in this disclosure areeach individually incorporated by reference herein in their entiretiesand as such are intended to provide an efficient way of supplementingthe enabling disclosure of this invention as well as provide backgrounddetailing the level of ordinary skill in the art.

The invention claimed is:
 1. A method of treating a tissue with amedical treatment device that applies electrical treatment energythrough one or more electrodes defining a target treatment area of thetissue and comprises a display device, the method comprising: providingone or more parameters of a treatment protocol for delivering one ormore electrical pulses to a tissue through one or more electrodes;modeling heat distribution and/or the electric field distribution in atissue surrounding the electrodes based on the one or more parametersand a treatment protocol-related change in electrical conductivity forthe target treatment are, which is a ratio of a maximum electricalconductivity that is reached during treatment to a baseline,non-electroporated, tissue-specific electrical conductivity; displayinga graphical representation of the heat and/or electric fielddistribution based on the modeled heat and/or electric fielddistribution in the display device; modifying one or more of theparameters of the treatment protocol based on the graphicalrepresentation of the heat and/or electric field distribution; andimplanting the electrodes in the tissue and delivering one or moreelectrical pulses to the tissue through the electrodes by way of avoltage pulse generator based on the one or more modified parameters. 2.The method of claim 1, wherein the one or more parameters are chosenfrom one or more of voltage, electrode spacing, electrode length,treatment duration, number of pulses, pulse width, electric fieldintensity, electrode diameter, a baseline conductivity for the targettreatment area, or a conductivity for a specific tissue type.
 3. Themethod of claim 1, wherein the treatment protocol-related change inelectrical conductivity is calculated in real time based on measuredvoltages and currents before, during, and/or after pulse delivery.
 4. Amethod of treatment planning for medical therapies involvingadministering electrical treatment energy, the method comprising:providing one or more parameters of a treatment protocol for deliveringone or more electrical pulses to tissue through one or more electrodes;modeling heat and/or electric field distribution in the tissue based onthe parameters and a treatment protocol-related change in electricalconductivity for the target treatment area, which is a ratio of amaximum electrical conductivity that is reached during treatment to abaseline, non-electroporated, tissue-specific electrical conductivity;and displaying a graphical representation of the modeled heat and/orelectric field distribution.
 5. The method of claim 4, wherein the heatdistribution is modeled to estimate the Joule heating in the tissue andis calculated as:${\rho\; C_{p}\frac{\partial T}{\partial t}} = {{\nabla{\cdot \left( {k{\nabla T}} \right)}} + {Q_{jh}\left\lbrack \frac{W}{m^{3}} \right\rbrack}}$where ρ is the density, C_(p) is the heat capacity, k is the thermalconductivity, and Q_(jh) are the resistive losses$Q_{jh} = {J \cdot {E\left\lbrack \frac{W}{m^{3}} \right\rbrack}}$ whereJ is the induced current density$J = {\sigma\;{E\left\lbrack \frac{A}{m^{2}} \right\rbrack}}$ and σ isthe tissue conductivity and E is the electric field$E = {- {{\nabla{\phi\left\lbrack \frac{V}{m} \right\rbrack}}.}}$
 6. Themethod of claim 4, further comprising specifying a cutoff heatdistribution value and providing a graphical representation of the heatand/or electric field distribution curve as an isocontour line.
 7. Themethod of claim 4, further comprising: modeling an electrical damageand/or a thermal damage in the tissue based on the parameters;displaying a graphical representation of the modeled electrical damageand/or thermal damage.
 8. The method of claim 7, wherein the electricfield distribution is calculated as:∇²ϕ=0 where ϕ is the electric potential, this equation is solved withboundary conditions: {right arrow over (n)}·{right arrow over (J)}=0 atthe boundaries ϕ=V_(in) at the boundary of the first electrode ϕ=0 atthe boundary of the second electrode wherein {right arrow over (n)} isthe normal vector to the surface, {right arrow over (J)} is theelectrical current and V_(in) is the electrical potential applied. 9.The method of claim 7, further comprising specifying a cutoff electricalfield distribution value and providing a graphical representation of theelectrical field distribution value as an isocontour line.
 10. Themethod of claim 9, further comprising one or more databases comprising aplurality of sets of parameters for treatment protocols stored in thedatabase.
 11. The method of claim 10, wherein the graphicalrepresentations of the modeled heat and electrical field distributionsare derived from Cassini oval calculations.
 12. The method of claim 7,wherein the graphical representation of the modeled thermal damageand/or electrical damage is derived from Cassini oval calculations. 13.The method of claim 4, wherein the parameters are chosen from one ormore of voltage, electrode spacing, electrode diameter, electrodelength, number of pulses, treatment duration, pulse width, electricfield intensity, a baseline conductivity for the target treatment area,or a conductivity for a specific tissue type.
 14. The method of claim 4,further comprising: modeling one or more of a thermally damaged region,IRE necrotic region, IRE apoptotic region, reversible electroporationregion, and region where there is no effect in the tissue based on theparameters; and displaying a graphical representation of the modeledregions.
 15. The method of claim 4, further comprising: modeling one ormore of a thermally damaged region, an electroporation region, and aregion where there is no effect in the tissue based on the parameters;and displaying a graphical representation of the modeled regions.
 16. Asystem for treatment planning for medical therapies involvingadministering electrical treatment energy, the system comprising: acomputer comprising: a memory; a display device; a processor coupled tothe memory and the display device; and a treatment planning modulestored in the memory and executable by the processor, the treatmentplanning module adapted to: receive as input one or more parameters of atreatment protocol for delivering one or more electrical pulses totissue through one or more electrodes; model heat and/or electric fielddistribution in the tissue based on the parameters and a treatmentprotocol-related change in electrical conductivity for the targettreatment area, which is a ratio of a maximum electrical conductivitythat is reached during treatment to a baseline, non-electroporated,tissue-specific electrical conductivity; display a graphicalrepresentation of the modeled heat and/or electric field distribution onthe display device.
 17. The system of claim 16, further comprising oneor more databases comprising a plurality of sets of parameters fortreatment protocols stored in the databases.
 18. The system of claim 16,wherein the inputs are chosen from one or more of voltage, electrodespacing, treatment duration, pulse width, electric field intensity, abaseline conductivity for the target treatment area, or a conductivityfor a specific tissue type.
 19. The system of claim 18, wherein theconductivity for a specific tissue type is provided in a database for aplurality of tissues.
 20. The system of claim 16, wherein the one ormore electrodes is provided by one or more bipolar probes.
 21. Thesystem of claim 16, wherein the one or more electrodes are provided byone or more single needle electrodes.